KILLED proof of input_uR9AmY0xlK.trs # AProVE Commit ID: aff8ecad908e01718a4c36e68d2e55d5e0f16e15 fuhs 20220216 unpublished The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) CpxTrsToCdtProof [UPPER BOUND(ID), 52 ms] (6) CdtProblem (7) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxRelTRS (9) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (10) TRS for Loop Detection (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxRelTRS (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (14) typed CpxTrs (15) OrderProof [LOWER BOUND(ID), 12 ms] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 712 ms] (18) typed CpxTrs (19) RelTrsToWeightedTrsProof [UPPER BOUND(ID), 0 ms] (20) CpxWeightedTrs (21) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (22) CpxTypedWeightedTrs (23) CompletionProof [UPPER BOUND(ID), 0 ms] (24) CpxTypedWeightedCompleteTrs (25) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (26) CpxRNTS (27) CompletionProof [UPPER BOUND(ID), 1 ms] (28) CpxTypedWeightedCompleteTrs (29) NarrowingProof [BOTH BOUNDS(ID, ID), 3854 ms] (30) CpxTypedWeightedCompleteTrs (31) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (32) CpxRNTS (33) InliningProof [UPPER BOUND(ID), 826 ms] (34) CpxRNTS (35) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (36) CpxRNTS (37) CpxTrsToCdtProof [UPPER BOUND(ID), 12 ms] (38) CdtProblem (39) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (40) CdtProblem (41) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (42) CdtProblem (43) CdtToCpxRelTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (44) CpxRelTRS (45) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (46) CpxTRS (47) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (48) CpxWeightedTrs (49) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (50) CpxTypedWeightedTrs (51) CompletionProof [UPPER BOUND(ID), 0 ms] (52) CpxTypedWeightedCompleteTrs (53) CompletionProof [UPPER BOUND(ID), 16 ms] (54) CpxTypedWeightedCompleteTrs (55) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 12 ms] (56) CpxRNTS (57) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (58) CdtProblem (59) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (60) CdtProblem (61) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (62) CdtProblem (63) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (64) CdtProblem (65) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 20 ms] (66) CdtProblem (67) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (68) CdtProblem (69) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (70) CdtProblem (71) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (72) CdtProblem (73) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (74) CdtProblem (75) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 11 ms] (76) CdtProblem (77) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (78) CdtProblem (79) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 13 ms] (80) CdtProblem (81) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (82) CdtProblem (83) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 20 ms] (84) CdtProblem (85) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (86) CdtProblem (87) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (88) CdtProblem (89) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (90) CdtProblem (91) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (92) CdtProblem (93) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 9 ms] (94) CdtProblem (95) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (96) CdtProblem (97) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 11 ms] (98) CdtProblem (99) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 8 ms] (100) CdtProblem (101) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (102) CdtProblem (103) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (104) CdtProblem (105) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 15 ms] (106) CdtProblem (107) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (108) CdtProblem (109) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 37 ms] (110) CdtProblem (111) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (112) CdtProblem (113) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (114) CdtProblem (115) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (116) CdtProblem (117) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 22 ms] (118) CdtProblem (119) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (120) CdtProblem (121) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 2 ms] (122) CdtProblem (123) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 8 ms] (124) CdtProblem (125) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 46 ms] (126) CdtProblem (127) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (128) CdtProblem (129) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (130) CdtProblem (131) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 59 ms] (132) CdtProblem (133) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (134) CdtProblem (135) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (136) CdtProblem (137) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 95 ms] (138) CdtProblem (139) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (140) CdtProblem (141) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (142) CdtProblem (143) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 126 ms] (144) CdtProblem (145) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 16 ms] (146) CdtProblem (147) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 148 ms] (148) CdtProblem (149) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (150) CdtProblem (151) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 22 ms] (152) CdtProblem (153) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 110 ms] (154) CdtProblem (155) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (156) CdtProblem (157) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 4 ms] (158) CdtProblem (159) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 106 ms] (160) CdtProblem (161) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 21 ms] (162) CdtProblem (163) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 9 ms] (164) CdtProblem (165) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 156 ms] (166) CdtProblem (167) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 4 ms] (168) CdtProblem (169) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 217 ms] (170) CdtProblem (171) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 35 ms] (172) CdtProblem (173) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 36 ms] (174) CdtProblem (175) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 53 ms] (176) CdtProblem (177) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 5 ms] (178) CdtProblem (179) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 33 ms] (180) CdtProblem (181) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (182) CdtProblem (183) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 53 ms] (184) CdtProblem (185) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 22 ms] (186) CdtProblem (187) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 156 ms] (188) CdtProblem (189) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (190) CdtProblem (191) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 169 ms] (192) CdtProblem (193) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 8 ms] (194) CdtProblem (195) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 103 ms] (196) CdtProblem (197) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (198) CdtProblem (199) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 181 ms] (200) CdtProblem (201) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 28 ms] (202) CdtProblem (203) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 172 ms] (204) CdtProblem (205) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 38 ms] (206) CdtProblem (207) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 180 ms] (208) CdtProblem (209) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 35 ms] (210) CdtProblem (211) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 153 ms] (212) CdtProblem (213) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 20 ms] (214) CdtProblem (215) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 162 ms] (216) CdtProblem (217) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 24 ms] (218) CdtProblem (219) CdtNarrowingProof [BOTH BOUNDS(ID, ID), 187 ms] (220) CdtProblem (221) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 25 ms] (222) CdtProblem ---------------------------------------- (0) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__U11(tt, V2) -> a__U12(a__isNat(V2)) a__U12(tt) -> tt a__U21(tt) -> tt a__U31(tt, V2) -> a__U32(a__isNat(V2)) a__U32(tt) -> tt a__U41(tt, N) -> mark(N) a__U51(tt, M, N) -> a__U52(a__isNat(N), M, N) a__U52(tt, M, N) -> s(a__plus(mark(N), mark(M))) a__U61(tt) -> 0 a__U71(tt, M, N) -> a__U72(a__isNat(N), M, N) a__U72(tt, M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N)) a__isNat(0) -> tt a__isNat(plus(V1, V2)) -> a__U11(a__isNat(V1), V2) a__isNat(s(V1)) -> a__U21(a__isNat(V1)) a__isNat(x(V1, V2)) -> a__U31(a__isNat(V1), V2) a__plus(N, 0) -> a__U41(a__isNat(N), N) a__plus(N, s(M)) -> a__U51(a__isNat(M), M, N) a__x(N, 0) -> a__U61(a__isNat(N)) a__x(N, s(M)) -> a__U71(a__isNat(M), M, N) mark(U11(X1, X2)) -> a__U11(mark(X1), X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNat(X)) -> a__isNat(X) mark(U21(X)) -> a__U21(mark(X)) mark(U31(X1, X2)) -> a__U31(mark(X1), X2) mark(U32(X)) -> a__U32(mark(X)) mark(U41(X1, X2)) -> a__U41(mark(X1), X2) mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3) mark(U52(X1, X2, X3)) -> a__U52(mark(X1), X2, X3) mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) mark(U61(X)) -> a__U61(mark(X)) mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3) mark(U72(X1, X2, X3)) -> a__U72(mark(X1), X2, X3) mark(x(X1, X2)) -> a__x(mark(X1), mark(X2)) mark(tt) -> tt mark(s(X)) -> s(mark(X)) mark(0) -> 0 a__U11(X1, X2) -> U11(X1, X2) a__U12(X) -> U12(X) a__isNat(X) -> isNat(X) a__U21(X) -> U21(X) a__U31(X1, X2) -> U31(X1, X2) a__U32(X) -> U32(X) a__U41(X1, X2) -> U41(X1, X2) a__U51(X1, X2, X3) -> U51(X1, X2, X3) a__U52(X1, X2, X3) -> U52(X1, X2, X3) a__plus(X1, X2) -> plus(X1, X2) a__U61(X) -> U61(X) a__U71(X1, X2, X3) -> U71(X1, X2, X3) a__U72(X1, X2, X3) -> U72(X1, X2, X3) a__x(X1, X2) -> x(X1, X2) S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (1) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (2) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__U11(tt, V2) -> a__U12(a__isNat(V2)) a__U12(tt) -> tt a__U21(tt) -> tt a__U31(tt, V2) -> a__U32(a__isNat(V2)) a__U32(tt) -> tt a__U41(tt, N) -> mark(N) a__U51(tt, M, N) -> a__U52(a__isNat(N), M, N) a__U52(tt, M, N) -> s(a__plus(mark(N), mark(M))) a__U61(tt) -> 0' a__U71(tt, M, N) -> a__U72(a__isNat(N), M, N) a__U72(tt, M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N)) a__isNat(0') -> tt a__isNat(plus(V1, V2)) -> a__U11(a__isNat(V1), V2) a__isNat(s(V1)) -> a__U21(a__isNat(V1)) a__isNat(x(V1, V2)) -> a__U31(a__isNat(V1), V2) a__plus(N, 0') -> a__U41(a__isNat(N), N) a__plus(N, s(M)) -> a__U51(a__isNat(M), M, N) a__x(N, 0') -> a__U61(a__isNat(N)) a__x(N, s(M)) -> a__U71(a__isNat(M), M, N) mark(U11(X1, X2)) -> a__U11(mark(X1), X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNat(X)) -> a__isNat(X) mark(U21(X)) -> a__U21(mark(X)) mark(U31(X1, X2)) -> a__U31(mark(X1), X2) mark(U32(X)) -> a__U32(mark(X)) mark(U41(X1, X2)) -> a__U41(mark(X1), X2) mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3) mark(U52(X1, X2, X3)) -> a__U52(mark(X1), X2, X3) mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) mark(U61(X)) -> a__U61(mark(X)) mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3) mark(U72(X1, X2, X3)) -> a__U72(mark(X1), X2, X3) mark(x(X1, X2)) -> a__x(mark(X1), mark(X2)) mark(tt) -> tt mark(s(X)) -> s(mark(X)) mark(0') -> 0' a__U11(X1, X2) -> U11(X1, X2) a__U12(X) -> U12(X) a__isNat(X) -> isNat(X) a__U21(X) -> U21(X) a__U31(X1, X2) -> U31(X1, X2) a__U32(X) -> U32(X) a__U41(X1, X2) -> U41(X1, X2) a__U51(X1, X2, X3) -> U51(X1, X2, X3) a__U52(X1, X2, X3) -> U52(X1, X2, X3) a__plus(X1, X2) -> plus(X1, X2) a__U61(X) -> U61(X) a__U71(X1, X2, X3) -> U71(X1, X2, X3) a__U72(X1, X2, X3) -> U72(X1, X2, X3) a__x(X1, X2) -> x(X1, X2) S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (3) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (4) Obligation: The Runtime Complexity (parallel-innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__U11(tt, V2) -> a__U12(a__isNat(V2)) a__U12(tt) -> tt a__U21(tt) -> tt a__U31(tt, V2) -> a__U32(a__isNat(V2)) a__U32(tt) -> tt a__U41(tt, N) -> mark(N) a__U51(tt, M, N) -> a__U52(a__isNat(N), M, N) a__U52(tt, M, N) -> s(a__plus(mark(N), mark(M))) a__U61(tt) -> 0 a__U71(tt, M, N) -> a__U72(a__isNat(N), M, N) a__U72(tt, M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N)) a__isNat(0) -> tt a__isNat(plus(V1, V2)) -> a__U11(a__isNat(V1), V2) a__isNat(s(V1)) -> a__U21(a__isNat(V1)) a__isNat(x(V1, V2)) -> a__U31(a__isNat(V1), V2) a__plus(N, 0) -> a__U41(a__isNat(N), N) a__plus(N, s(M)) -> a__U51(a__isNat(M), M, N) a__x(N, 0) -> a__U61(a__isNat(N)) a__x(N, s(M)) -> a__U71(a__isNat(M), M, N) mark(U11(X1, X2)) -> a__U11(mark(X1), X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNat(X)) -> a__isNat(X) mark(U21(X)) -> a__U21(mark(X)) mark(U31(X1, X2)) -> a__U31(mark(X1), X2) mark(U32(X)) -> a__U32(mark(X)) mark(U41(X1, X2)) -> a__U41(mark(X1), X2) mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3) mark(U52(X1, X2, X3)) -> a__U52(mark(X1), X2, X3) mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) mark(U61(X)) -> a__U61(mark(X)) mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3) mark(U72(X1, X2, X3)) -> a__U72(mark(X1), X2, X3) mark(x(X1, X2)) -> a__x(mark(X1), mark(X2)) mark(tt) -> tt mark(s(X)) -> s(mark(X)) mark(0) -> 0 a__U11(X1, X2) -> U11(X1, X2) a__U12(X) -> U12(X) a__isNat(X) -> isNat(X) a__U21(X) -> U21(X) a__U31(X1, X2) -> U31(X1, X2) a__U32(X) -> U32(X) a__U41(X1, X2) -> U41(X1, X2) a__U51(X1, X2, X3) -> U51(X1, X2, X3) a__U52(X1, X2, X3) -> U52(X1, X2, X3) a__plus(X1, X2) -> plus(X1, X2) a__U61(X) -> U61(X) a__U71(X1, X2, X3) -> U71(X1, X2, X3) a__U72(X1, X2, X3) -> U72(X1, X2, X3) a__x(X1, X2) -> x(X1, X2) S is empty. Rewrite Strategy: PARALLEL_INNERMOST ---------------------------------------- (5) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (6) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(A__U12(a__isNat(z0)), A__ISNAT(z0)) A__U11(z0, z1) -> c1 A__U12(tt) -> c2 A__U12(z0) -> c3 A__U21(tt) -> c4 A__U21(z0) -> c5 A__U31(tt, z0) -> c6(A__U32(a__isNat(z0)), A__ISNAT(z0)) A__U31(z0, z1) -> c7 A__U32(tt) -> c8 A__U32(z0) -> c9 A__U41(tt, z0) -> c10(MARK(z0)) A__U41(z0, z1) -> c11 A__U51(tt, z0, z1) -> c12(A__U52(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U51(z0, z1, z2) -> c13 A__U52(tt, z0, z1) -> c14(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U52(tt, z0, z1) -> c15(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U52(z0, z1, z2) -> c16 A__U61(tt) -> c17 A__U61(z0) -> c18 A__U71(tt, z0, z1) -> c19(A__U72(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U71(z0, z1, z2) -> c20 A__U72(tt, z0, z1) -> c21(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) A__U72(tt, z0, z1) -> c22(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) A__U72(z0, z1, z2) -> c24 A__ISNAT(0) -> c25 A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__U21(a__isNat(z0)), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(z0) -> c29 A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__PLUS(z0, z1) -> c32 A__X(z0, 0) -> c33(A__U61(a__isNat(z0)), A__ISNAT(z0)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, z1) -> c35 MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c37(A__U12(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U21(z0)) -> c39(A__U21(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U32(z0)) -> c41(A__U32(mark(z0)), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U61(z0)) -> c47(A__U61(mark(z0)), MARK(z0)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c52 MARK(s(z0)) -> c53(MARK(z0)) MARK(0) -> c54 S tuples: A__U11(tt, z0) -> c(A__U12(a__isNat(z0)), A__ISNAT(z0)) A__U11(z0, z1) -> c1 A__U12(tt) -> c2 A__U12(z0) -> c3 A__U21(tt) -> c4 A__U21(z0) -> c5 A__U31(tt, z0) -> c6(A__U32(a__isNat(z0)), A__ISNAT(z0)) A__U31(z0, z1) -> c7 A__U32(tt) -> c8 A__U32(z0) -> c9 A__U41(tt, z0) -> c10(MARK(z0)) A__U41(z0, z1) -> c11 A__U51(tt, z0, z1) -> c12(A__U52(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U51(z0, z1, z2) -> c13 A__U52(tt, z0, z1) -> c14(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U52(tt, z0, z1) -> c15(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U52(z0, z1, z2) -> c16 A__U61(tt) -> c17 A__U61(z0) -> c18 A__U71(tt, z0, z1) -> c19(A__U72(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U71(z0, z1, z2) -> c20 A__U72(tt, z0, z1) -> c21(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) A__U72(tt, z0, z1) -> c22(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) A__U72(z0, z1, z2) -> c24 A__ISNAT(0) -> c25 A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__U21(a__isNat(z0)), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(z0) -> c29 A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__PLUS(z0, z1) -> c32 A__X(z0, 0) -> c33(A__U61(a__isNat(z0)), A__ISNAT(z0)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, z1) -> c35 MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c37(A__U12(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U21(z0)) -> c39(A__U21(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U32(z0)) -> c41(A__U32(mark(z0)), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U61(z0)) -> c47(A__U61(mark(z0)), MARK(z0)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c52 MARK(s(z0)) -> c53(MARK(z0)) MARK(0) -> c54 K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U11_2, A__U12_1, A__U21_1, A__U31_2, A__U32_1, A__U41_2, A__U51_3, A__U52_3, A__U61_1, A__U71_3, A__U72_3, A__ISNAT_1, A__PLUS_2, A__X_2, MARK_1 Compound Symbols: c_2, c1, c2, c3, c4, c5, c6_2, c7, c8, c9, c10_1, c11, c12_2, c13, c14_2, c15_2, c16, c17, c18, c19_2, c20, c21_3, c22_3, c23_2, c24, c25, c26_2, c27_2, c28_2, c29, c30_2, c31_2, c32, c33_2, c34_2, c35, c36_2, c37_2, c38_1, c39_2, c40_2, c41_2, c42_2, c43_2, c44_2, c45_2, c46_2, c47_2, c48_2, c49_2, c50_2, c51_2, c52, c53_1, c54 ---------------------------------------- (7) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID)) Converted S to standard rules, and D \ S as well as R to relative rules. ---------------------------------------- (8) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__U11(tt, z0) -> c(A__U12(a__isNat(z0)), A__ISNAT(z0)) A__U11(z0, z1) -> c1 A__U12(tt) -> c2 A__U12(z0) -> c3 A__U21(tt) -> c4 A__U21(z0) -> c5 A__U31(tt, z0) -> c6(A__U32(a__isNat(z0)), A__ISNAT(z0)) A__U31(z0, z1) -> c7 A__U32(tt) -> c8 A__U32(z0) -> c9 A__U41(tt, z0) -> c10(MARK(z0)) A__U41(z0, z1) -> c11 A__U51(tt, z0, z1) -> c12(A__U52(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U51(z0, z1, z2) -> c13 A__U52(tt, z0, z1) -> c14(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U52(tt, z0, z1) -> c15(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U52(z0, z1, z2) -> c16 A__U61(tt) -> c17 A__U61(z0) -> c18 A__U71(tt, z0, z1) -> c19(A__U72(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U71(z0, z1, z2) -> c20 A__U72(tt, z0, z1) -> c21(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) A__U72(tt, z0, z1) -> c22(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) A__U72(z0, z1, z2) -> c24 A__ISNAT(0) -> c25 A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__U21(a__isNat(z0)), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(z0) -> c29 A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__PLUS(z0, z1) -> c32 A__X(z0, 0) -> c33(A__U61(a__isNat(z0)), A__ISNAT(z0)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, z1) -> c35 MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c37(A__U12(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U21(z0)) -> c39(A__U21(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U32(z0)) -> c41(A__U32(mark(z0)), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U61(z0)) -> c47(A__U61(mark(z0)), MARK(z0)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c52 MARK(s(z0)) -> c53(MARK(z0)) MARK(0) -> c54 The (relative) TRS S consists of the following rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Rewrite Strategy: INNERMOST ---------------------------------------- (9) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (10) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__U11(tt, z0) -> c(A__U12(a__isNat(z0)), A__ISNAT(z0)) A__U11(z0, z1) -> c1 A__U12(tt) -> c2 A__U12(z0) -> c3 A__U21(tt) -> c4 A__U21(z0) -> c5 A__U31(tt, z0) -> c6(A__U32(a__isNat(z0)), A__ISNAT(z0)) A__U31(z0, z1) -> c7 A__U32(tt) -> c8 A__U32(z0) -> c9 A__U41(tt, z0) -> c10(MARK(z0)) A__U41(z0, z1) -> c11 A__U51(tt, z0, z1) -> c12(A__U52(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U51(z0, z1, z2) -> c13 A__U52(tt, z0, z1) -> c14(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U52(tt, z0, z1) -> c15(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U52(z0, z1, z2) -> c16 A__U61(tt) -> c17 A__U61(z0) -> c18 A__U71(tt, z0, z1) -> c19(A__U72(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U71(z0, z1, z2) -> c20 A__U72(tt, z0, z1) -> c21(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) A__U72(tt, z0, z1) -> c22(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) A__U72(z0, z1, z2) -> c24 A__ISNAT(0) -> c25 A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__U21(a__isNat(z0)), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(z0) -> c29 A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__PLUS(z0, z1) -> c32 A__X(z0, 0) -> c33(A__U61(a__isNat(z0)), A__ISNAT(z0)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, z1) -> c35 MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c37(A__U12(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U21(z0)) -> c39(A__U21(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U32(z0)) -> c41(A__U32(mark(z0)), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U61(z0)) -> c47(A__U61(mark(z0)), MARK(z0)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c52 MARK(s(z0)) -> c53(MARK(z0)) MARK(0) -> c54 The (relative) TRS S consists of the following rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Rewrite Strategy: INNERMOST ---------------------------------------- (11) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (12) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__U11(tt, z0) -> c(A__U12(a__isNat(z0)), A__ISNAT(z0)) A__U11(z0, z1) -> c1 A__U12(tt) -> c2 A__U12(z0) -> c3 A__U21(tt) -> c4 A__U21(z0) -> c5 A__U31(tt, z0) -> c6(A__U32(a__isNat(z0)), A__ISNAT(z0)) A__U31(z0, z1) -> c7 A__U32(tt) -> c8 A__U32(z0) -> c9 A__U41(tt, z0) -> c10(MARK(z0)) A__U41(z0, z1) -> c11 A__U51(tt, z0, z1) -> c12(A__U52(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U51(z0, z1, z2) -> c13 A__U52(tt, z0, z1) -> c14(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U52(tt, z0, z1) -> c15(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U52(z0, z1, z2) -> c16 A__U61(tt) -> c17 A__U61(z0) -> c18 A__U71(tt, z0, z1) -> c19(A__U72(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U71(z0, z1, z2) -> c20 A__U72(tt, z0, z1) -> c21(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) A__U72(tt, z0, z1) -> c22(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) A__U72(z0, z1, z2) -> c24 A__ISNAT(0') -> c25 A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__U21(a__isNat(z0)), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(z0) -> c29 A__PLUS(z0, 0') -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__PLUS(z0, z1) -> c32 A__X(z0, 0') -> c33(A__U61(a__isNat(z0)), A__ISNAT(z0)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, z1) -> c35 MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c37(A__U12(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U21(z0)) -> c39(A__U21(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U32(z0)) -> c41(A__U32(mark(z0)), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U61(z0)) -> c47(A__U61(mark(z0)), MARK(z0)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c52 MARK(s(z0)) -> c53(MARK(z0)) MARK(0') -> c54 The (relative) TRS S consists of the following rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0' a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0') -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0') -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0') -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0') -> 0' Rewrite Strategy: INNERMOST ---------------------------------------- (13) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Inferred types. ---------------------------------------- (14) Obligation: Innermost TRS: Rules: A__U11(tt, z0) -> c(A__U12(a__isNat(z0)), A__ISNAT(z0)) A__U11(z0, z1) -> c1 A__U12(tt) -> c2 A__U12(z0) -> c3 A__U21(tt) -> c4 A__U21(z0) -> c5 A__U31(tt, z0) -> c6(A__U32(a__isNat(z0)), A__ISNAT(z0)) A__U31(z0, z1) -> c7 A__U32(tt) -> c8 A__U32(z0) -> c9 A__U41(tt, z0) -> c10(MARK(z0)) A__U41(z0, z1) -> c11 A__U51(tt, z0, z1) -> c12(A__U52(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U51(z0, z1, z2) -> c13 A__U52(tt, z0, z1) -> c14(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U52(tt, z0, z1) -> c15(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U52(z0, z1, z2) -> c16 A__U61(tt) -> c17 A__U61(z0) -> c18 A__U71(tt, z0, z1) -> c19(A__U72(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U71(z0, z1, z2) -> c20 A__U72(tt, z0, z1) -> c21(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) A__U72(tt, z0, z1) -> c22(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) A__U72(z0, z1, z2) -> c24 A__ISNAT(0') -> c25 A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__U21(a__isNat(z0)), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(z0) -> c29 A__PLUS(z0, 0') -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__PLUS(z0, z1) -> c32 A__X(z0, 0') -> c33(A__U61(a__isNat(z0)), A__ISNAT(z0)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, z1) -> c35 MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c37(A__U12(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U21(z0)) -> c39(A__U21(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U32(z0)) -> c41(A__U32(mark(z0)), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U61(z0)) -> c47(A__U61(mark(z0)), MARK(z0)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c52 MARK(s(z0)) -> c53(MARK(z0)) MARK(0') -> c54 a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0' a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0') -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0') -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0') -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0') -> 0' Types: A__U11 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c:c1 tt :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c :: c2:c3 -> c25:c26:c27:c28:c29 -> c:c1 A__U12 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c2:c3 a__isNat :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 A__ISNAT :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c25:c26:c27:c28:c29 c1 :: c:c1 c2 :: c2:c3 c3 :: c2:c3 A__U21 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c4:c5 c4 :: c4:c5 c5 :: c4:c5 A__U31 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c6:c7 c6 :: c8:c9 -> c25:c26:c27:c28:c29 -> c6:c7 A__U32 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c8:c9 c7 :: c6:c7 c8 :: c8:c9 c9 :: c8:c9 A__U41 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c10:c11 c10 :: c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c10:c11 MARK :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 c11 :: c10:c11 A__U51 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c12:c13 c12 :: c14:c15:c16 -> c25:c26:c27:c28:c29 -> c12:c13 A__U52 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c14:c15:c16 c13 :: c12:c13 c14 :: c30:c31:c32 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c14:c15:c16 A__PLUS :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c30:c31:c32 mark :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c15 :: c30:c31:c32 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c14:c15:c16 c16 :: c14:c15:c16 A__U61 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c17:c18 c17 :: c17:c18 c18 :: c17:c18 A__U71 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c19:c20 c19 :: c21:c22:c23:c24 -> c25:c26:c27:c28:c29 -> c19:c20 A__U72 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c21:c22:c23:c24 c20 :: c19:c20 c21 :: c30:c31:c32 -> c33:c34:c35 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c21:c22:c23:c24 a__x :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 A__X :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c33:c34:c35 c22 :: c30:c31:c32 -> c33:c34:c35 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c21:c22:c23:c24 c23 :: c30:c31:c32 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c21:c22:c23:c24 c24 :: c21:c22:c23:c24 0' :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c25 :: c25:c26:c27:c28:c29 plus :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c26 :: c:c1 -> c25:c26:c27:c28:c29 -> c25:c26:c27:c28:c29 s :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c27 :: c4:c5 -> c25:c26:c27:c28:c29 -> c25:c26:c27:c28:c29 x :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c28 :: c6:c7 -> c25:c26:c27:c28:c29 -> c25:c26:c27:c28:c29 c29 :: c25:c26:c27:c28:c29 c30 :: c10:c11 -> c25:c26:c27:c28:c29 -> c30:c31:c32 c31 :: c12:c13 -> c25:c26:c27:c28:c29 -> c30:c31:c32 c32 :: c30:c31:c32 c33 :: c17:c18 -> c25:c26:c27:c28:c29 -> c33:c34:c35 c34 :: c19:c20 -> c25:c26:c27:c28:c29 -> c33:c34:c35 c35 :: c33:c34:c35 U11 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c36 :: c:c1 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 U12 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c37 :: c2:c3 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 isNat :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c38 :: c25:c26:c27:c28:c29 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 U21 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c39 :: c4:c5 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 U31 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c40 :: c6:c7 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 U32 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c41 :: c8:c9 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 U41 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c42 :: c10:c11 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 U51 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c43 :: c12:c13 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 U52 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c44 :: c14:c15:c16 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 c45 :: c30:c31:c32 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 c46 :: c30:c31:c32 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 U61 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c47 :: c17:c18 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 U71 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c48 :: c19:c20 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 U72 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c49 :: c21:c22:c23:c24 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 c50 :: c33:c34:c35 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 c51 :: c33:c34:c35 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 c52 :: c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 c53 :: c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 c54 :: c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 a__U11 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U12 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U21 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U31 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U32 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U41 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U51 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U52 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__plus :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U61 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U71 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U72 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 hole_c:c11_55 :: c:c1 hole_tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U722_55 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 hole_c2:c33_55 :: c2:c3 hole_c25:c26:c27:c28:c294_55 :: c25:c26:c27:c28:c29 hole_c4:c55_55 :: c4:c5 hole_c6:c76_55 :: c6:c7 hole_c8:c97_55 :: c8:c9 hole_c10:c118_55 :: c10:c11 hole_c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c549_55 :: c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 hole_c12:c1310_55 :: c12:c13 hole_c14:c15:c1611_55 :: c14:c15:c16 hole_c30:c31:c3212_55 :: c30:c31:c32 hole_c17:c1813_55 :: c17:c18 hole_c19:c2014_55 :: c19:c20 hole_c21:c22:c23:c2415_55 :: c21:c22:c23:c24 hole_c33:c34:c3516_55 :: c33:c34:c35 gen_tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U7217_55 :: Nat -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 gen_c25:c26:c27:c28:c2918_55 :: Nat -> c25:c26:c27:c28:c29 gen_c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c5419_55 :: Nat -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 ---------------------------------------- (15) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: A__U11, a__isNat, A__ISNAT, A__U31, A__U41, MARK, A__U51, A__U52, A__PLUS, mark, A__U71, A__U72, a__x, A__X, a__U11, a__U31, a__U41, a__U51, a__U52, a__plus, a__U71, a__U72 They will be analysed ascendingly in the following order: a__isNat < A__U11 A__U11 = A__ISNAT A__U11 = A__U31 A__U11 < MARK a__isNat < A__ISNAT a__isNat < A__U31 a__isNat < A__U51 a__isNat < A__PLUS a__isNat < mark a__isNat < A__U71 a__isNat < a__x a__isNat < A__X a__isNat = a__U11 a__isNat = a__U31 a__isNat < a__U51 a__isNat < a__plus a__isNat < a__U71 A__ISNAT = A__U31 A__ISNAT < MARK A__ISNAT < A__U51 A__ISNAT < A__PLUS A__ISNAT < A__U71 A__ISNAT < A__X A__U31 < MARK A__U41 = MARK A__U41 = A__U51 A__U41 = A__U52 A__U41 = A__PLUS A__U41 = A__U71 A__U41 = A__U72 A__U41 = A__X MARK = A__U51 MARK = A__U52 MARK = A__PLUS mark < MARK MARK = A__U71 MARK = A__U72 MARK = A__X A__U51 = A__U52 A__U51 = A__PLUS A__U51 = A__U71 A__U51 = A__U72 A__U51 = A__X A__U52 = A__PLUS mark < A__U52 A__U52 = A__U71 A__U52 = A__U72 A__U52 = A__X A__PLUS = A__U71 A__PLUS = A__U72 A__PLUS = A__X mark < A__U72 mark = a__x a__U11 < mark a__U31 < mark mark = a__U41 mark = a__U51 mark = a__U52 mark = a__plus mark = a__U71 mark = a__U72 A__U71 = A__U72 A__U71 = A__X a__x < A__U72 A__U72 = A__X a__x = a__U41 a__x = a__U51 a__x = a__U52 a__x = a__plus a__x = a__U71 a__x = a__U72 a__U11 = a__U31 a__U41 = a__U51 a__U41 = a__U52 a__U41 = a__plus a__U41 = a__U71 a__U41 = a__U72 a__U51 = a__U52 a__U51 = a__plus a__U51 = a__U71 a__U51 = a__U72 a__U52 = a__plus a__U52 = a__U71 a__U52 = a__U72 a__plus = a__U71 a__plus = a__U72 a__U71 = a__U72 ---------------------------------------- (16) Obligation: Innermost TRS: Rules: A__U11(tt, z0) -> c(A__U12(a__isNat(z0)), A__ISNAT(z0)) A__U11(z0, z1) -> c1 A__U12(tt) -> c2 A__U12(z0) -> c3 A__U21(tt) -> c4 A__U21(z0) -> c5 A__U31(tt, z0) -> c6(A__U32(a__isNat(z0)), A__ISNAT(z0)) A__U31(z0, z1) -> c7 A__U32(tt) -> c8 A__U32(z0) -> c9 A__U41(tt, z0) -> c10(MARK(z0)) A__U41(z0, z1) -> c11 A__U51(tt, z0, z1) -> c12(A__U52(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U51(z0, z1, z2) -> c13 A__U52(tt, z0, z1) -> c14(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U52(tt, z0, z1) -> c15(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U52(z0, z1, z2) -> c16 A__U61(tt) -> c17 A__U61(z0) -> c18 A__U71(tt, z0, z1) -> c19(A__U72(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U71(z0, z1, z2) -> c20 A__U72(tt, z0, z1) -> c21(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) A__U72(tt, z0, z1) -> c22(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) A__U72(z0, z1, z2) -> c24 A__ISNAT(0') -> c25 A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__U21(a__isNat(z0)), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(z0) -> c29 A__PLUS(z0, 0') -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__PLUS(z0, z1) -> c32 A__X(z0, 0') -> c33(A__U61(a__isNat(z0)), A__ISNAT(z0)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, z1) -> c35 MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c37(A__U12(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U21(z0)) -> c39(A__U21(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U32(z0)) -> c41(A__U32(mark(z0)), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U61(z0)) -> c47(A__U61(mark(z0)), MARK(z0)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c52 MARK(s(z0)) -> c53(MARK(z0)) MARK(0') -> c54 a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0' a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0') -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0') -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0') -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0') -> 0' Types: A__U11 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c:c1 tt :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c :: c2:c3 -> c25:c26:c27:c28:c29 -> c:c1 A__U12 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c2:c3 a__isNat :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 A__ISNAT :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c25:c26:c27:c28:c29 c1 :: c:c1 c2 :: c2:c3 c3 :: c2:c3 A__U21 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c4:c5 c4 :: c4:c5 c5 :: c4:c5 A__U31 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c6:c7 c6 :: c8:c9 -> c25:c26:c27:c28:c29 -> c6:c7 A__U32 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c8:c9 c7 :: c6:c7 c8 :: c8:c9 c9 :: c8:c9 A__U41 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c10:c11 c10 :: c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c10:c11 MARK :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 c11 :: c10:c11 A__U51 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c12:c13 c12 :: c14:c15:c16 -> c25:c26:c27:c28:c29 -> c12:c13 A__U52 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c14:c15:c16 c13 :: c12:c13 c14 :: c30:c31:c32 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c14:c15:c16 A__PLUS :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c30:c31:c32 mark :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c15 :: c30:c31:c32 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c14:c15:c16 c16 :: c14:c15:c16 A__U61 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c17:c18 c17 :: c17:c18 c18 :: c17:c18 A__U71 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c19:c20 c19 :: c21:c22:c23:c24 -> c25:c26:c27:c28:c29 -> c19:c20 A__U72 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c21:c22:c23:c24 c20 :: c19:c20 c21 :: c30:c31:c32 -> c33:c34:c35 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c21:c22:c23:c24 a__x :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 A__X :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c33:c34:c35 c22 :: c30:c31:c32 -> c33:c34:c35 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c21:c22:c23:c24 c23 :: c30:c31:c32 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c21:c22:c23:c24 c24 :: c21:c22:c23:c24 0' :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c25 :: c25:c26:c27:c28:c29 plus :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c26 :: c:c1 -> c25:c26:c27:c28:c29 -> c25:c26:c27:c28:c29 s :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c27 :: c4:c5 -> c25:c26:c27:c28:c29 -> c25:c26:c27:c28:c29 x :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c28 :: c6:c7 -> c25:c26:c27:c28:c29 -> c25:c26:c27:c28:c29 c29 :: c25:c26:c27:c28:c29 c30 :: c10:c11 -> c25:c26:c27:c28:c29 -> c30:c31:c32 c31 :: c12:c13 -> c25:c26:c27:c28:c29 -> c30:c31:c32 c32 :: c30:c31:c32 c33 :: c17:c18 -> c25:c26:c27:c28:c29 -> c33:c34:c35 c34 :: c19:c20 -> c25:c26:c27:c28:c29 -> c33:c34:c35 c35 :: c33:c34:c35 U11 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c36 :: c:c1 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 U12 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c37 :: c2:c3 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 isNat :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c38 :: c25:c26:c27:c28:c29 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 U21 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c39 :: c4:c5 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 U31 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c40 :: c6:c7 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 U32 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c41 :: c8:c9 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 U41 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c42 :: c10:c11 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 U51 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c43 :: c12:c13 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 U52 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c44 :: c14:c15:c16 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 c45 :: c30:c31:c32 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 c46 :: c30:c31:c32 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 U61 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c47 :: c17:c18 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 U71 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c48 :: c19:c20 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 U72 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c49 :: c21:c22:c23:c24 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 c50 :: c33:c34:c35 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 c51 :: c33:c34:c35 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 c52 :: c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 c53 :: c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 c54 :: c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 a__U11 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U12 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U21 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U31 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U32 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U41 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U51 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U52 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__plus :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U61 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U71 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U72 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 hole_c:c11_55 :: c:c1 hole_tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U722_55 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 hole_c2:c33_55 :: c2:c3 hole_c25:c26:c27:c28:c294_55 :: c25:c26:c27:c28:c29 hole_c4:c55_55 :: c4:c5 hole_c6:c76_55 :: c6:c7 hole_c8:c97_55 :: c8:c9 hole_c10:c118_55 :: c10:c11 hole_c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c549_55 :: c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 hole_c12:c1310_55 :: c12:c13 hole_c14:c15:c1611_55 :: c14:c15:c16 hole_c30:c31:c3212_55 :: c30:c31:c32 hole_c17:c1813_55 :: c17:c18 hole_c19:c2014_55 :: c19:c20 hole_c21:c22:c23:c2415_55 :: c21:c22:c23:c24 hole_c33:c34:c3516_55 :: c33:c34:c35 gen_tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U7217_55 :: Nat -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 gen_c25:c26:c27:c28:c2918_55 :: Nat -> c25:c26:c27:c28:c29 gen_c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c5419_55 :: Nat -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 Generator Equations: gen_tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U7217_55(0) <=> tt gen_tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U7217_55(+(x, 1)) <=> plus(gen_tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U7217_55(x), tt) gen_c25:c26:c27:c28:c2918_55(0) <=> c25 gen_c25:c26:c27:c28:c2918_55(+(x, 1)) <=> c26(c(c2, c25), gen_c25:c26:c27:c28:c2918_55(x)) gen_c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c5419_55(0) <=> c38(c25) gen_c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c5419_55(+(x, 1)) <=> c36(c(c2, c25), gen_c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c5419_55(x)) The following defined symbols remain to be analysed: a__U11, A__U11, a__isNat, A__ISNAT, A__U31, A__U41, MARK, A__U51, A__U52, A__PLUS, mark, A__U71, A__U72, a__x, A__X, a__U31, a__U41, a__U51, a__U52, a__plus, a__U71, a__U72 They will be analysed ascendingly in the following order: a__isNat < A__U11 A__U11 = A__ISNAT A__U11 = A__U31 A__U11 < MARK a__isNat < A__ISNAT a__isNat < A__U31 a__isNat < A__U51 a__isNat < A__PLUS a__isNat < mark a__isNat < A__U71 a__isNat < a__x a__isNat < A__X a__isNat = a__U11 a__isNat = a__U31 a__isNat < a__U51 a__isNat < a__plus a__isNat < a__U71 A__ISNAT = A__U31 A__ISNAT < MARK A__ISNAT < A__U51 A__ISNAT < A__PLUS A__ISNAT < A__U71 A__ISNAT < A__X A__U31 < MARK A__U41 = MARK A__U41 = A__U51 A__U41 = A__U52 A__U41 = A__PLUS A__U41 = A__U71 A__U41 = A__U72 A__U41 = A__X MARK = A__U51 MARK = A__U52 MARK = A__PLUS mark < MARK MARK = A__U71 MARK = A__U72 MARK = A__X A__U51 = A__U52 A__U51 = A__PLUS A__U51 = A__U71 A__U51 = A__U72 A__U51 = A__X A__U52 = A__PLUS mark < A__U52 A__U52 = A__U71 A__U52 = A__U72 A__U52 = A__X A__PLUS = A__U71 A__PLUS = A__U72 A__PLUS = A__X mark < A__U72 mark = a__x a__U11 < mark a__U31 < mark mark = a__U41 mark = a__U51 mark = a__U52 mark = a__plus mark = a__U71 mark = a__U72 A__U71 = A__U72 A__U71 = A__X a__x < A__U72 A__U72 = A__X a__x = a__U41 a__x = a__U51 a__x = a__U52 a__x = a__plus a__x = a__U71 a__x = a__U72 a__U11 = a__U31 a__U41 = a__U51 a__U41 = a__U52 a__U41 = a__plus a__U41 = a__U71 a__U41 = a__U72 a__U51 = a__U52 a__U51 = a__plus a__U51 = a__U71 a__U51 = a__U72 a__U52 = a__plus a__U52 = a__U71 a__U52 = a__U72 a__plus = a__U71 a__plus = a__U72 a__U71 = a__U72 ---------------------------------------- (17) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: a__isNat(gen_tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U7217_55(+(1, n2649_55))) -> *20_55, rt in Omega(0) Induction Base: a__isNat(gen_tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U7217_55(+(1, 0))) Induction Step: a__isNat(gen_tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U7217_55(+(1, +(n2649_55, 1)))) ->_R^Omega(0) a__U11(a__isNat(gen_tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U7217_55(+(1, n2649_55))), tt) ->_IH a__U11(*20_55, tt) We have rt in Omega(1) and sz in O(n). Thus, we have irc_R in Omega(n^0). ---------------------------------------- (18) Obligation: Innermost TRS: Rules: A__U11(tt, z0) -> c(A__U12(a__isNat(z0)), A__ISNAT(z0)) A__U11(z0, z1) -> c1 A__U12(tt) -> c2 A__U12(z0) -> c3 A__U21(tt) -> c4 A__U21(z0) -> c5 A__U31(tt, z0) -> c6(A__U32(a__isNat(z0)), A__ISNAT(z0)) A__U31(z0, z1) -> c7 A__U32(tt) -> c8 A__U32(z0) -> c9 A__U41(tt, z0) -> c10(MARK(z0)) A__U41(z0, z1) -> c11 A__U51(tt, z0, z1) -> c12(A__U52(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U51(z0, z1, z2) -> c13 A__U52(tt, z0, z1) -> c14(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U52(tt, z0, z1) -> c15(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U52(z0, z1, z2) -> c16 A__U61(tt) -> c17 A__U61(z0) -> c18 A__U71(tt, z0, z1) -> c19(A__U72(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U71(z0, z1, z2) -> c20 A__U72(tt, z0, z1) -> c21(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) A__U72(tt, z0, z1) -> c22(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) A__U72(z0, z1, z2) -> c24 A__ISNAT(0') -> c25 A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__U21(a__isNat(z0)), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(z0) -> c29 A__PLUS(z0, 0') -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__PLUS(z0, z1) -> c32 A__X(z0, 0') -> c33(A__U61(a__isNat(z0)), A__ISNAT(z0)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, z1) -> c35 MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c37(A__U12(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U21(z0)) -> c39(A__U21(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U32(z0)) -> c41(A__U32(mark(z0)), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U61(z0)) -> c47(A__U61(mark(z0)), MARK(z0)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c52 MARK(s(z0)) -> c53(MARK(z0)) MARK(0') -> c54 a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0' a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0') -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0') -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0') -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0') -> 0' Types: A__U11 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c:c1 tt :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c :: c2:c3 -> c25:c26:c27:c28:c29 -> c:c1 A__U12 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c2:c3 a__isNat :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 A__ISNAT :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c25:c26:c27:c28:c29 c1 :: c:c1 c2 :: c2:c3 c3 :: c2:c3 A__U21 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c4:c5 c4 :: c4:c5 c5 :: c4:c5 A__U31 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c6:c7 c6 :: c8:c9 -> c25:c26:c27:c28:c29 -> c6:c7 A__U32 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c8:c9 c7 :: c6:c7 c8 :: c8:c9 c9 :: c8:c9 A__U41 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c10:c11 c10 :: c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c10:c11 MARK :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 c11 :: c10:c11 A__U51 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c12:c13 c12 :: c14:c15:c16 -> c25:c26:c27:c28:c29 -> c12:c13 A__U52 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c14:c15:c16 c13 :: c12:c13 c14 :: c30:c31:c32 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c14:c15:c16 A__PLUS :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c30:c31:c32 mark :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c15 :: c30:c31:c32 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c14:c15:c16 c16 :: c14:c15:c16 A__U61 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c17:c18 c17 :: c17:c18 c18 :: c17:c18 A__U71 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c19:c20 c19 :: c21:c22:c23:c24 -> c25:c26:c27:c28:c29 -> c19:c20 A__U72 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c21:c22:c23:c24 c20 :: c19:c20 c21 :: c30:c31:c32 -> c33:c34:c35 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c21:c22:c23:c24 a__x :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 A__X :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> c33:c34:c35 c22 :: c30:c31:c32 -> c33:c34:c35 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c21:c22:c23:c24 c23 :: c30:c31:c32 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c21:c22:c23:c24 c24 :: c21:c22:c23:c24 0' :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c25 :: c25:c26:c27:c28:c29 plus :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c26 :: c:c1 -> c25:c26:c27:c28:c29 -> c25:c26:c27:c28:c29 s :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c27 :: c4:c5 -> c25:c26:c27:c28:c29 -> c25:c26:c27:c28:c29 x :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c28 :: c6:c7 -> c25:c26:c27:c28:c29 -> c25:c26:c27:c28:c29 c29 :: c25:c26:c27:c28:c29 c30 :: c10:c11 -> c25:c26:c27:c28:c29 -> c30:c31:c32 c31 :: c12:c13 -> c25:c26:c27:c28:c29 -> c30:c31:c32 c32 :: c30:c31:c32 c33 :: c17:c18 -> c25:c26:c27:c28:c29 -> c33:c34:c35 c34 :: c19:c20 -> c25:c26:c27:c28:c29 -> c33:c34:c35 c35 :: c33:c34:c35 U11 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c36 :: c:c1 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 U12 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c37 :: c2:c3 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 isNat :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c38 :: c25:c26:c27:c28:c29 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 U21 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c39 :: c4:c5 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 U31 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c40 :: c6:c7 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 U32 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c41 :: c8:c9 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 U41 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c42 :: c10:c11 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 U51 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c43 :: c12:c13 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 U52 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c44 :: c14:c15:c16 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 c45 :: c30:c31:c32 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 c46 :: c30:c31:c32 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 U61 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c47 :: c17:c18 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 U71 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c48 :: c19:c20 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 U72 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 c49 :: c21:c22:c23:c24 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 c50 :: c33:c34:c35 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 c51 :: c33:c34:c35 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 c52 :: c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 c53 :: c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 c54 :: c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 a__U11 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U12 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U21 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U31 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U32 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U41 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U51 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U52 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__plus :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U61 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U71 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U72 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 hole_c:c11_55 :: c:c1 hole_tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U722_55 :: tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 hole_c2:c33_55 :: c2:c3 hole_c25:c26:c27:c28:c294_55 :: c25:c26:c27:c28:c29 hole_c4:c55_55 :: c4:c5 hole_c6:c76_55 :: c6:c7 hole_c8:c97_55 :: c8:c9 hole_c10:c118_55 :: c10:c11 hole_c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c549_55 :: c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 hole_c12:c1310_55 :: c12:c13 hole_c14:c15:c1611_55 :: c14:c15:c16 hole_c30:c31:c3212_55 :: c30:c31:c32 hole_c17:c1813_55 :: c17:c18 hole_c19:c2014_55 :: c19:c20 hole_c21:c22:c23:c2415_55 :: c21:c22:c23:c24 hole_c33:c34:c3516_55 :: c33:c34:c35 gen_tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U7217_55 :: Nat -> tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 gen_c25:c26:c27:c28:c2918_55 :: Nat -> c25:c26:c27:c28:c29 gen_c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c5419_55 :: Nat -> c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c54 Lemmas: a__isNat(gen_tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U7217_55(+(1, n2649_55))) -> *20_55, rt in Omega(0) Generator Equations: gen_tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U7217_55(0) <=> tt gen_tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U7217_55(+(x, 1)) <=> plus(gen_tt:0':plus:s:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U7217_55(x), tt) gen_c25:c26:c27:c28:c2918_55(0) <=> c25 gen_c25:c26:c27:c28:c2918_55(+(x, 1)) <=> c26(c(c2, c25), gen_c25:c26:c27:c28:c2918_55(x)) gen_c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c5419_55(0) <=> c38(c25) gen_c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c5419_55(+(x, 1)) <=> c36(c(c2, c25), gen_c36:c37:c38:c39:c40:c41:c42:c43:c44:c45:c46:c47:c48:c49:c50:c51:c52:c53:c5419_55(x)) The following defined symbols remain to be analysed: a__U31, A__U11, A__ISNAT, A__U31, A__U41, MARK, A__U51, A__U52, A__PLUS, mark, A__U71, A__U72, a__x, A__X, a__U11, a__U41, a__U51, a__U52, a__plus, a__U71, a__U72 They will be analysed ascendingly in the following order: a__isNat < A__U11 A__U11 = A__ISNAT A__U11 = A__U31 A__U11 < MARK a__isNat < A__ISNAT a__isNat < A__U31 a__isNat < A__U51 a__isNat < A__PLUS a__isNat < mark a__isNat < A__U71 a__isNat < a__x a__isNat < A__X a__isNat = a__U11 a__isNat = a__U31 a__isNat < a__U51 a__isNat < a__plus a__isNat < a__U71 A__ISNAT = A__U31 A__ISNAT < MARK A__ISNAT < A__U51 A__ISNAT < A__PLUS A__ISNAT < A__U71 A__ISNAT < A__X A__U31 < MARK A__U41 = MARK A__U41 = A__U51 A__U41 = A__U52 A__U41 = A__PLUS A__U41 = A__U71 A__U41 = A__U72 A__U41 = A__X MARK = A__U51 MARK = A__U52 MARK = A__PLUS mark < MARK MARK = A__U71 MARK = A__U72 MARK = A__X A__U51 = A__U52 A__U51 = A__PLUS A__U51 = A__U71 A__U51 = A__U72 A__U51 = A__X A__U52 = A__PLUS mark < A__U52 A__U52 = A__U71 A__U52 = A__U72 A__U52 = A__X A__PLUS = A__U71 A__PLUS = A__U72 A__PLUS = A__X mark < A__U72 mark = a__x a__U11 < mark a__U31 < mark mark = a__U41 mark = a__U51 mark = a__U52 mark = a__plus mark = a__U71 mark = a__U72 A__U71 = A__U72 A__U71 = A__X a__x < A__U72 A__U72 = A__X a__x = a__U41 a__x = a__U51 a__x = a__U52 a__x = a__plus a__x = a__U71 a__x = a__U72 a__U11 = a__U31 a__U41 = a__U51 a__U41 = a__U52 a__U41 = a__plus a__U41 = a__U71 a__U41 = a__U72 a__U51 = a__U52 a__U51 = a__plus a__U51 = a__U71 a__U51 = a__U72 a__U52 = a__plus a__U52 = a__U71 a__U52 = a__U72 a__plus = a__U71 a__plus = a__U72 a__U71 = a__U72 ---------------------------------------- (19) RelTrsToWeightedTrsProof (UPPER BOUND(ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (20) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: a__U11(tt, V2) -> a__U12(a__isNat(V2)) [1] a__U12(tt) -> tt [1] a__U21(tt) -> tt [1] a__U31(tt, V2) -> a__U32(a__isNat(V2)) [1] a__U32(tt) -> tt [1] a__U41(tt, N) -> mark(N) [1] a__U51(tt, M, N) -> a__U52(a__isNat(N), M, N) [1] a__U52(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1] a__U61(tt) -> 0 [1] a__U71(tt, M, N) -> a__U72(a__isNat(N), M, N) [1] a__U72(tt, M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N)) [1] a__isNat(0) -> tt [1] a__isNat(plus(V1, V2)) -> a__U11(a__isNat(V1), V2) [1] a__isNat(s(V1)) -> a__U21(a__isNat(V1)) [1] a__isNat(x(V1, V2)) -> a__U31(a__isNat(V1), V2) [1] a__plus(N, 0) -> a__U41(a__isNat(N), N) [1] a__plus(N, s(M)) -> a__U51(a__isNat(M), M, N) [1] a__x(N, 0) -> a__U61(a__isNat(N)) [1] a__x(N, s(M)) -> a__U71(a__isNat(M), M, N) [1] mark(U11(X1, X2)) -> a__U11(mark(X1), X2) [1] mark(U12(X)) -> a__U12(mark(X)) [1] mark(isNat(X)) -> a__isNat(X) [1] mark(U21(X)) -> a__U21(mark(X)) [1] mark(U31(X1, X2)) -> a__U31(mark(X1), X2) [1] mark(U32(X)) -> a__U32(mark(X)) [1] mark(U41(X1, X2)) -> a__U41(mark(X1), X2) [1] mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3) [1] mark(U52(X1, X2, X3)) -> a__U52(mark(X1), X2, X3) [1] mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1] mark(U61(X)) -> a__U61(mark(X)) [1] mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3) [1] mark(U72(X1, X2, X3)) -> a__U72(mark(X1), X2, X3) [1] mark(x(X1, X2)) -> a__x(mark(X1), mark(X2)) [1] mark(tt) -> tt [1] mark(s(X)) -> s(mark(X)) [1] mark(0) -> 0 [1] a__U11(X1, X2) -> U11(X1, X2) [1] a__U12(X) -> U12(X) [1] a__isNat(X) -> isNat(X) [1] a__U21(X) -> U21(X) [1] a__U31(X1, X2) -> U31(X1, X2) [1] a__U32(X) -> U32(X) [1] a__U41(X1, X2) -> U41(X1, X2) [1] a__U51(X1, X2, X3) -> U51(X1, X2, X3) [1] a__U52(X1, X2, X3) -> U52(X1, X2, X3) [1] a__plus(X1, X2) -> plus(X1, X2) [1] a__U61(X) -> U61(X) [1] a__U71(X1, X2, X3) -> U71(X1, X2, X3) [1] a__U72(X1, X2, X3) -> U72(X1, X2, X3) [1] a__x(X1, X2) -> x(X1, X2) [1] Rewrite Strategy: INNERMOST ---------------------------------------- (21) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (22) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__U11(tt, V2) -> a__U12(a__isNat(V2)) [1] a__U12(tt) -> tt [1] a__U21(tt) -> tt [1] a__U31(tt, V2) -> a__U32(a__isNat(V2)) [1] a__U32(tt) -> tt [1] a__U41(tt, N) -> mark(N) [1] a__U51(tt, M, N) -> a__U52(a__isNat(N), M, N) [1] a__U52(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1] a__U61(tt) -> 0 [1] a__U71(tt, M, N) -> a__U72(a__isNat(N), M, N) [1] a__U72(tt, M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N)) [1] a__isNat(0) -> tt [1] a__isNat(plus(V1, V2)) -> a__U11(a__isNat(V1), V2) [1] a__isNat(s(V1)) -> a__U21(a__isNat(V1)) [1] a__isNat(x(V1, V2)) -> a__U31(a__isNat(V1), V2) [1] a__plus(N, 0) -> a__U41(a__isNat(N), N) [1] a__plus(N, s(M)) -> a__U51(a__isNat(M), M, N) [1] a__x(N, 0) -> a__U61(a__isNat(N)) [1] a__x(N, s(M)) -> a__U71(a__isNat(M), M, N) [1] mark(U11(X1, X2)) -> a__U11(mark(X1), X2) [1] mark(U12(X)) -> a__U12(mark(X)) [1] mark(isNat(X)) -> a__isNat(X) [1] mark(U21(X)) -> a__U21(mark(X)) [1] mark(U31(X1, X2)) -> a__U31(mark(X1), X2) [1] mark(U32(X)) -> a__U32(mark(X)) [1] mark(U41(X1, X2)) -> a__U41(mark(X1), X2) [1] mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3) [1] mark(U52(X1, X2, X3)) -> a__U52(mark(X1), X2, X3) [1] mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1] mark(U61(X)) -> a__U61(mark(X)) [1] mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3) [1] mark(U72(X1, X2, X3)) -> a__U72(mark(X1), X2, X3) [1] mark(x(X1, X2)) -> a__x(mark(X1), mark(X2)) [1] mark(tt) -> tt [1] mark(s(X)) -> s(mark(X)) [1] mark(0) -> 0 [1] a__U11(X1, X2) -> U11(X1, X2) [1] a__U12(X) -> U12(X) [1] a__isNat(X) -> isNat(X) [1] a__U21(X) -> U21(X) [1] a__U31(X1, X2) -> U31(X1, X2) [1] a__U32(X) -> U32(X) [1] a__U41(X1, X2) -> U41(X1, X2) [1] a__U51(X1, X2, X3) -> U51(X1, X2, X3) [1] a__U52(X1, X2, X3) -> U52(X1, X2, X3) [1] a__plus(X1, X2) -> plus(X1, X2) [1] a__U61(X) -> U61(X) [1] a__U71(X1, X2, X3) -> U71(X1, X2, X3) [1] a__U72(X1, X2, X3) -> U72(X1, X2, X3) [1] a__x(X1, X2) -> x(X1, X2) [1] The TRS has the following type information: a__U11 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 tt :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U12 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__isNat :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U21 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U31 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U32 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U41 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 mark :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U51 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U52 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 s :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__plus :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U61 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 0 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U71 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U72 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__x :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 plus :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 x :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 U11 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 U12 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 isNat :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 U21 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 U31 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 U32 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 U41 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 U51 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 U52 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 U61 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 U71 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 U72 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 Rewrite Strategy: INNERMOST ---------------------------------------- (23) CompletionProof (UPPER BOUND(ID)) The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: none And the following fresh constants: none ---------------------------------------- (24) Obligation: Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__U11(tt, V2) -> a__U12(a__isNat(V2)) [1] a__U12(tt) -> tt [1] a__U21(tt) -> tt [1] a__U31(tt, V2) -> a__U32(a__isNat(V2)) [1] a__U32(tt) -> tt [1] a__U41(tt, N) -> mark(N) [1] a__U51(tt, M, N) -> a__U52(a__isNat(N), M, N) [1] a__U52(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1] a__U61(tt) -> 0 [1] a__U71(tt, M, N) -> a__U72(a__isNat(N), M, N) [1] a__U72(tt, M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N)) [1] a__isNat(0) -> tt [1] a__isNat(plus(V1, V2)) -> a__U11(a__isNat(V1), V2) [1] a__isNat(s(V1)) -> a__U21(a__isNat(V1)) [1] a__isNat(x(V1, V2)) -> a__U31(a__isNat(V1), V2) [1] a__plus(N, 0) -> a__U41(a__isNat(N), N) [1] a__plus(N, s(M)) -> a__U51(a__isNat(M), M, N) [1] a__x(N, 0) -> a__U61(a__isNat(N)) [1] a__x(N, s(M)) -> a__U71(a__isNat(M), M, N) [1] mark(U11(X1, X2)) -> a__U11(mark(X1), X2) [1] mark(U12(X)) -> a__U12(mark(X)) [1] mark(isNat(X)) -> a__isNat(X) [1] mark(U21(X)) -> a__U21(mark(X)) [1] mark(U31(X1, X2)) -> a__U31(mark(X1), X2) [1] mark(U32(X)) -> a__U32(mark(X)) [1] mark(U41(X1, X2)) -> a__U41(mark(X1), X2) [1] mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3) [1] mark(U52(X1, X2, X3)) -> a__U52(mark(X1), X2, X3) [1] mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1] mark(U61(X)) -> a__U61(mark(X)) [1] mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3) [1] mark(U72(X1, X2, X3)) -> a__U72(mark(X1), X2, X3) [1] mark(x(X1, X2)) -> a__x(mark(X1), mark(X2)) [1] mark(tt) -> tt [1] mark(s(X)) -> s(mark(X)) [1] mark(0) -> 0 [1] a__U11(X1, X2) -> U11(X1, X2) [1] a__U12(X) -> U12(X) [1] a__isNat(X) -> isNat(X) [1] a__U21(X) -> U21(X) [1] a__U31(X1, X2) -> U31(X1, X2) [1] a__U32(X) -> U32(X) [1] a__U41(X1, X2) -> U41(X1, X2) [1] a__U51(X1, X2, X3) -> U51(X1, X2, X3) [1] a__U52(X1, X2, X3) -> U52(X1, X2, X3) [1] a__plus(X1, X2) -> plus(X1, X2) [1] a__U61(X) -> U61(X) [1] a__U71(X1, X2, X3) -> U71(X1, X2, X3) [1] a__U72(X1, X2, X3) -> U72(X1, X2, X3) [1] a__x(X1, X2) -> x(X1, X2) [1] The TRS has the following type information: a__U11 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 tt :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U12 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__isNat :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U21 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U31 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U32 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U41 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 mark :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U51 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U52 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 s :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__plus :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U61 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 0 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U71 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U72 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__x :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 plus :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 x :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 U11 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 U12 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 isNat :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 U21 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 U31 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 U32 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 U41 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 U51 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 U52 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 U61 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 U71 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 U72 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 Rewrite Strategy: INNERMOST ---------------------------------------- (25) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: tt => 1 0 => 0 ---------------------------------------- (26) Obligation: Complexity RNTS consisting of the following rules: a__U11(z, z') -{ 1 }-> a__U12(a__isNat(V2)) :|: z' = V2, z = 1, V2 >= 0 a__U11(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U12(z) -{ 1 }-> 1 :|: z = 1 a__U12(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U21(z) -{ 1 }-> 1 :|: z = 1 a__U21(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U31(z, z') -{ 1 }-> a__U32(a__isNat(V2)) :|: z' = V2, z = 1, V2 >= 0 a__U31(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U32(z) -{ 1 }-> 1 :|: z = 1 a__U32(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U41(z, z') -{ 1 }-> mark(N) :|: z = 1, z' = N, N >= 0 a__U41(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U51(z, z', z'') -{ 1 }-> a__U52(a__isNat(N), M, N) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0 a__U51(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U52(z, z', z'') -{ 1 }-> 1 + a__plus(mark(N), mark(M)) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0 a__U52(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U61(z) -{ 1 }-> 0 :|: z = 1 a__U61(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U71(z, z', z'') -{ 1 }-> a__U72(a__isNat(N), M, N) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0 a__U71(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U72(z, z', z'') -{ 1 }-> a__plus(a__x(mark(N), mark(M)), mark(N)) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0 a__U72(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__isNat(z) -{ 1 }-> a__U31(a__isNat(V1), V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNat(z) -{ 1 }-> a__U21(a__isNat(V1)) :|: z = 1 + V1, V1 >= 0 a__isNat(z) -{ 1 }-> a__U11(a__isNat(V1), V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNat(z) -{ 1 }-> 1 :|: z = 0 a__isNat(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__plus(z, z') -{ 1 }-> a__U51(a__isNat(M), M, N) :|: z' = 1 + M, z = N, M >= 0, N >= 0 a__plus(z, z') -{ 1 }-> a__U41(a__isNat(N), N) :|: z = N, z' = 0, N >= 0 a__plus(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__x(z, z') -{ 1 }-> a__U71(a__isNat(M), M, N) :|: z' = 1 + M, z = N, M >= 0, N >= 0 a__x(z, z') -{ 1 }-> a__U61(a__isNat(N)) :|: z = N, z' = 0, N >= 0 a__x(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 mark(z) -{ 1 }-> a__x(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__plus(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__isNat(X) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U72(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U71(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U61(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U52(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U51(mark(X1), X2, X3) :|: X1 >= 0, X3 >= 0, z = 1 + X1 + X2 + X3, X2 >= 0 mark(z) -{ 1 }-> a__U41(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U32(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U31(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__U21(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U12(mark(X)) :|: z = 1 + X, X >= 0 mark(z) -{ 1 }-> a__U11(mark(X1), X2) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (27) CompletionProof (UPPER BOUND(ID)) The transformation into a RNTS is sound, since: (a) The obligation is a constructor system where every type has a constant constructor, (b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols: none (c) The following functions are completely defined: mark_1 a__isNat_1 a__x_2 a__U32_1 a__U52_3 a__U21_1 a__U31_2 a__U72_3 a__U11_2 a__U61_1 a__U71_3 a__U41_2 a__U12_1 a__plus_2 a__U51_3 Due to the following rules being added: none And the following fresh constants: none ---------------------------------------- (28) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__U11(tt, V2) -> a__U12(a__isNat(V2)) [1] a__U12(tt) -> tt [1] a__U21(tt) -> tt [1] a__U31(tt, V2) -> a__U32(a__isNat(V2)) [1] a__U32(tt) -> tt [1] a__U41(tt, N) -> mark(N) [1] a__U51(tt, M, N) -> a__U52(a__isNat(N), M, N) [1] a__U52(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1] a__U61(tt) -> 0 [1] a__U71(tt, M, N) -> a__U72(a__isNat(N), M, N) [1] a__U72(tt, M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N)) [1] a__isNat(0) -> tt [1] a__isNat(plus(V1, V2)) -> a__U11(a__isNat(V1), V2) [1] a__isNat(s(V1)) -> a__U21(a__isNat(V1)) [1] a__isNat(x(V1, V2)) -> a__U31(a__isNat(V1), V2) [1] a__plus(N, 0) -> a__U41(a__isNat(N), N) [1] a__plus(N, s(M)) -> a__U51(a__isNat(M), M, N) [1] a__x(N, 0) -> a__U61(a__isNat(N)) [1] a__x(N, s(M)) -> a__U71(a__isNat(M), M, N) [1] mark(U11(X1, X2)) -> a__U11(mark(X1), X2) [1] mark(U12(X)) -> a__U12(mark(X)) [1] mark(isNat(X)) -> a__isNat(X) [1] mark(U21(X)) -> a__U21(mark(X)) [1] mark(U31(X1, X2)) -> a__U31(mark(X1), X2) [1] mark(U32(X)) -> a__U32(mark(X)) [1] mark(U41(X1, X2)) -> a__U41(mark(X1), X2) [1] mark(U51(X1, X2, X3)) -> a__U51(mark(X1), X2, X3) [1] mark(U52(X1, X2, X3)) -> a__U52(mark(X1), X2, X3) [1] mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1] mark(U61(X)) -> a__U61(mark(X)) [1] mark(U71(X1, X2, X3)) -> a__U71(mark(X1), X2, X3) [1] mark(U72(X1, X2, X3)) -> a__U72(mark(X1), X2, X3) [1] mark(x(X1, X2)) -> a__x(mark(X1), mark(X2)) [1] mark(tt) -> tt [1] mark(s(X)) -> s(mark(X)) [1] mark(0) -> 0 [1] a__U11(X1, X2) -> U11(X1, X2) [1] a__U12(X) -> U12(X) [1] a__isNat(X) -> isNat(X) [1] a__U21(X) -> U21(X) [1] a__U31(X1, X2) -> U31(X1, X2) [1] a__U32(X) -> U32(X) [1] a__U41(X1, X2) -> U41(X1, X2) [1] a__U51(X1, X2, X3) -> U51(X1, X2, X3) [1] a__U52(X1, X2, X3) -> U52(X1, X2, X3) [1] a__plus(X1, X2) -> plus(X1, X2) [1] a__U61(X) -> U61(X) [1] a__U71(X1, X2, X3) -> U71(X1, X2, X3) [1] a__U72(X1, X2, X3) -> U72(X1, X2, X3) [1] a__x(X1, X2) -> x(X1, X2) [1] The TRS has the following type information: a__U11 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 tt :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U12 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__isNat :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U21 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U31 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U32 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U41 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 mark :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U51 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U52 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 s :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__plus :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U61 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 0 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U71 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U72 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__x :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 plus :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 x :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 U11 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 U12 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 isNat :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 U21 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 U31 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 U32 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 U41 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 U51 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 U52 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 U61 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 U71 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 U72 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 Rewrite Strategy: INNERMOST ---------------------------------------- (29) NarrowingProof (BOTH BOUNDS(ID, ID)) Narrowed the inner basic terms of all right-hand sides by a single narrowing step. ---------------------------------------- (30) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: a__U11(tt, 0) -> a__U12(tt) [2] a__U11(tt, plus(V1', V2')) -> a__U12(a__U11(a__isNat(V1'), V2')) [2] a__U11(tt, s(V1'')) -> a__U12(a__U21(a__isNat(V1''))) [2] a__U11(tt, x(V11, V2'')) -> a__U12(a__U31(a__isNat(V11), V2'')) [2] a__U11(tt, V2) -> a__U12(isNat(V2)) [2] a__U12(tt) -> tt [1] a__U21(tt) -> tt [1] a__U31(tt, 0) -> a__U32(tt) [2] a__U31(tt, plus(V12, V21)) -> a__U32(a__U11(a__isNat(V12), V21)) [2] a__U31(tt, s(V13)) -> a__U32(a__U21(a__isNat(V13))) [2] a__U31(tt, x(V14, V22)) -> a__U32(a__U31(a__isNat(V14), V22)) [2] a__U31(tt, V2) -> a__U32(isNat(V2)) [2] a__U32(tt) -> tt [1] a__U41(tt, N) -> mark(N) [1] a__U51(tt, M, 0) -> a__U52(tt, M, 0) [2] a__U51(tt, M, plus(V15, V23)) -> a__U52(a__U11(a__isNat(V15), V23), M, plus(V15, V23)) [2] a__U51(tt, M, s(V16)) -> a__U52(a__U21(a__isNat(V16)), M, s(V16)) [2] a__U51(tt, M, x(V17, V24)) -> a__U52(a__U31(a__isNat(V17), V24), M, x(V17, V24)) [2] a__U51(tt, M, N) -> a__U52(isNat(N), M, N) [2] a__U52(tt, M, N) -> s(a__plus(mark(N), mark(M))) [1] a__U61(tt) -> 0 [1] a__U71(tt, M, 0) -> a__U72(tt, M, 0) [2] a__U71(tt, M, plus(V18, V25)) -> a__U72(a__U11(a__isNat(V18), V25), M, plus(V18, V25)) [2] a__U71(tt, M, s(V19)) -> a__U72(a__U21(a__isNat(V19)), M, s(V19)) [2] a__U71(tt, M, x(V110, V26)) -> a__U72(a__U31(a__isNat(V110), V26), M, x(V110, V26)) [2] a__U71(tt, M, N) -> a__U72(isNat(N), M, N) [2] a__U72(tt, M, N) -> a__plus(a__x(mark(N), mark(M)), mark(N)) [1] a__isNat(0) -> tt [1] a__isNat(plus(0, V2)) -> a__U11(tt, V2) [2] a__isNat(plus(plus(V111, V27), V2)) -> a__U11(a__U11(a__isNat(V111), V27), V2) [2] a__isNat(plus(s(V112), V2)) -> a__U11(a__U21(a__isNat(V112)), V2) [2] a__isNat(plus(x(V113, V28), V2)) -> a__U11(a__U31(a__isNat(V113), V28), V2) [2] a__isNat(plus(V1, V2)) -> a__U11(isNat(V1), V2) [2] a__isNat(s(0)) -> a__U21(tt) [2] a__isNat(s(plus(V114, V29))) -> a__U21(a__U11(a__isNat(V114), V29)) [2] a__isNat(s(s(V115))) -> a__U21(a__U21(a__isNat(V115))) [2] a__isNat(s(x(V116, V210))) -> a__U21(a__U31(a__isNat(V116), V210)) [2] a__isNat(s(V1)) -> a__U21(isNat(V1)) [2] a__isNat(x(0, V2)) -> a__U31(tt, V2) [2] a__isNat(x(plus(V117, V211), V2)) -> a__U31(a__U11(a__isNat(V117), V211), V2) [2] a__isNat(x(s(V118), V2)) -> a__U31(a__U21(a__isNat(V118)), V2) [2] a__isNat(x(x(V119, V212), V2)) -> a__U31(a__U31(a__isNat(V119), V212), V2) [2] a__isNat(x(V1, V2)) -> a__U31(isNat(V1), V2) [2] a__plus(0, 0) -> a__U41(tt, 0) [2] a__plus(plus(V120, V213), 0) -> a__U41(a__U11(a__isNat(V120), V213), plus(V120, V213)) [2] a__plus(s(V121), 0) -> a__U41(a__U21(a__isNat(V121)), s(V121)) [2] a__plus(x(V122, V214), 0) -> a__U41(a__U31(a__isNat(V122), V214), x(V122, V214)) [2] a__plus(N, 0) -> a__U41(isNat(N), N) [2] a__plus(N, s(0)) -> a__U51(tt, 0, N) [2] a__plus(N, s(plus(V123, V215))) -> a__U51(a__U11(a__isNat(V123), V215), plus(V123, V215), N) [2] a__plus(N, s(s(V124))) -> a__U51(a__U21(a__isNat(V124)), s(V124), N) [2] a__plus(N, s(x(V125, V216))) -> a__U51(a__U31(a__isNat(V125), V216), x(V125, V216), N) [2] a__plus(N, s(M)) -> a__U51(isNat(M), M, N) [2] a__x(0, 0) -> a__U61(tt) [2] a__x(plus(V126, V217), 0) -> a__U61(a__U11(a__isNat(V126), V217)) [2] a__x(s(V127), 0) -> a__U61(a__U21(a__isNat(V127))) [2] a__x(x(V128, V218), 0) -> a__U61(a__U31(a__isNat(V128), V218)) [2] a__x(N, 0) -> a__U61(isNat(N)) [2] a__x(N, s(0)) -> a__U71(tt, 0, N) [2] a__x(N, s(plus(V129, V219))) -> a__U71(a__U11(a__isNat(V129), V219), plus(V129, V219), N) [2] a__x(N, s(s(V130))) -> a__U71(a__U21(a__isNat(V130)), s(V130), N) [2] a__x(N, s(x(V131, V220))) -> a__U71(a__U31(a__isNat(V131), V220), x(V131, V220), N) [2] a__x(N, s(M)) -> a__U71(isNat(M), M, N) [2] mark(U11(U11(X1323, X2323), X2)) -> a__U11(a__U11(mark(X1323), X2323), X2) [2] mark(U11(U12(X494), X2)) -> a__U11(a__U12(mark(X494)), X2) [2] mark(U11(isNat(X495), X2)) -> a__U11(a__isNat(X495), X2) [2] mark(U11(U21(X496), X2)) -> a__U11(a__U21(mark(X496)), X2) [2] mark(U11(U31(X1324, X2324), X2)) -> a__U11(a__U31(mark(X1324), X2324), X2) [2] mark(U11(U32(X497), X2)) -> a__U11(a__U32(mark(X497)), X2) [2] mark(U11(U41(X1325, X2325), X2)) -> a__U11(a__U41(mark(X1325), X2325), X2) [2] mark(U11(U51(X1326, X2326, X3164), X2)) -> a__U11(a__U51(mark(X1326), X2326, X3164), X2) [2] mark(U11(U52(X1327, X2327, X3165), X2)) -> a__U11(a__U52(mark(X1327), X2327, X3165), X2) [2] mark(U11(plus(X1328, X2328), X2)) -> a__U11(a__plus(mark(X1328), mark(X2328)), X2) [2] mark(U11(U61(X498), X2)) -> a__U11(a__U61(mark(X498)), X2) [2] mark(U11(U71(X1329, X2329, X3166), X2)) -> a__U11(a__U71(mark(X1329), X2329, X3166), X2) [2] mark(U11(U72(X1330, X2330, X3167), X2)) -> a__U11(a__U72(mark(X1330), X2330, X3167), X2) [2] mark(U11(x(X1331, X2331), X2)) -> a__U11(a__x(mark(X1331), mark(X2331)), X2) [2] mark(U11(tt, X2)) -> a__U11(tt, X2) [2] mark(U11(s(X499), X2)) -> a__U11(s(mark(X499)), X2) [2] mark(U11(0, X2)) -> a__U11(0, X2) [2] mark(U12(U11(X1332, X2332))) -> a__U12(a__U11(mark(X1332), X2332)) [2] mark(U12(U12(X500))) -> a__U12(a__U12(mark(X500))) [2] mark(U12(isNat(X501))) -> a__U12(a__isNat(X501)) [2] mark(U12(U21(X502))) -> a__U12(a__U21(mark(X502))) [2] mark(U12(U31(X1333, X2333))) -> a__U12(a__U31(mark(X1333), X2333)) [2] mark(U12(U32(X503))) -> a__U12(a__U32(mark(X503))) [2] mark(U12(U41(X1334, X2334))) -> a__U12(a__U41(mark(X1334), X2334)) [2] mark(U12(U51(X1335, X2335, X3168))) -> a__U12(a__U51(mark(X1335), X2335, X3168)) [2] mark(U12(U52(X1336, X2336, X3169))) -> a__U12(a__U52(mark(X1336), X2336, X3169)) [2] mark(U12(plus(X1337, X2337))) -> a__U12(a__plus(mark(X1337), mark(X2337))) [2] mark(U12(U61(X504))) -> a__U12(a__U61(mark(X504))) [2] mark(U12(U71(X1338, X2338, X3170))) -> a__U12(a__U71(mark(X1338), X2338, X3170)) [2] mark(U12(U72(X1339, X2339, X3171))) -> a__U12(a__U72(mark(X1339), X2339, X3171)) [2] mark(U12(x(X1340, X2340))) -> a__U12(a__x(mark(X1340), mark(X2340))) [2] mark(U12(tt)) -> a__U12(tt) [2] mark(U12(s(X505))) -> a__U12(s(mark(X505))) [2] mark(U12(0)) -> a__U12(0) [2] mark(isNat(X)) -> a__isNat(X) [1] mark(U21(U11(X1341, X2341))) -> a__U21(a__U11(mark(X1341), X2341)) [2] mark(U21(U12(X506))) -> a__U21(a__U12(mark(X506))) [2] mark(U21(isNat(X507))) -> a__U21(a__isNat(X507)) [2] mark(U21(U21(X508))) -> a__U21(a__U21(mark(X508))) [2] mark(U21(U31(X1342, X2342))) -> a__U21(a__U31(mark(X1342), X2342)) [2] mark(U21(U32(X509))) -> a__U21(a__U32(mark(X509))) [2] mark(U21(U41(X1343, X2343))) -> a__U21(a__U41(mark(X1343), X2343)) [2] mark(U21(U51(X1344, X2344, X3172))) -> a__U21(a__U51(mark(X1344), X2344, X3172)) [2] mark(U21(U52(X1345, X2345, X3173))) -> a__U21(a__U52(mark(X1345), X2345, X3173)) [2] mark(U21(plus(X1346, X2346))) -> a__U21(a__plus(mark(X1346), mark(X2346))) [2] mark(U21(U61(X510))) -> a__U21(a__U61(mark(X510))) [2] mark(U21(U71(X1347, X2347, X3174))) -> a__U21(a__U71(mark(X1347), X2347, X3174)) [2] mark(U21(U72(X1348, X2348, X3175))) -> a__U21(a__U72(mark(X1348), X2348, X3175)) [2] mark(U21(x(X1349, X2349))) -> a__U21(a__x(mark(X1349), mark(X2349))) [2] mark(U21(tt)) -> a__U21(tt) [2] mark(U21(s(X511))) -> a__U21(s(mark(X511))) [2] mark(U21(0)) -> a__U21(0) [2] mark(U31(U11(X1350, X2350), X2)) -> a__U31(a__U11(mark(X1350), X2350), X2) [2] mark(U31(U12(X512), X2)) -> a__U31(a__U12(mark(X512)), X2) [2] mark(U31(isNat(X513), X2)) -> a__U31(a__isNat(X513), X2) [2] mark(U31(U21(X514), X2)) -> a__U31(a__U21(mark(X514)), X2) [2] mark(U31(U31(X1351, X2351), X2)) -> a__U31(a__U31(mark(X1351), X2351), X2) [2] mark(U31(U32(X515), X2)) -> a__U31(a__U32(mark(X515)), X2) [2] mark(U31(U41(X1352, X2352), X2)) -> a__U31(a__U41(mark(X1352), X2352), X2) [2] mark(U31(U51(X1353, X2353, X3176), X2)) -> a__U31(a__U51(mark(X1353), X2353, X3176), X2) [2] mark(U31(U52(X1354, X2354, X3177), X2)) -> a__U31(a__U52(mark(X1354), X2354, X3177), X2) [2] mark(U31(plus(X1355, X2355), X2)) -> a__U31(a__plus(mark(X1355), mark(X2355)), X2) [2] mark(U31(U61(X516), X2)) -> a__U31(a__U61(mark(X516)), X2) [2] mark(U31(U71(X1356, X2356, X3178), X2)) -> a__U31(a__U71(mark(X1356), X2356, X3178), X2) [2] mark(U31(U72(X1357, X2357, X3179), X2)) -> a__U31(a__U72(mark(X1357), X2357, X3179), X2) [2] mark(U31(x(X1358, X2358), X2)) -> a__U31(a__x(mark(X1358), mark(X2358)), X2) [2] mark(U31(tt, X2)) -> a__U31(tt, X2) [2] mark(U31(s(X517), X2)) -> a__U31(s(mark(X517)), X2) [2] mark(U31(0, X2)) -> a__U31(0, X2) [2] mark(U32(U11(X1359, X2359))) -> a__U32(a__U11(mark(X1359), X2359)) [2] mark(U32(U12(X518))) -> a__U32(a__U12(mark(X518))) [2] mark(U32(isNat(X519))) -> a__U32(a__isNat(X519)) [2] mark(U32(U21(X520))) -> a__U32(a__U21(mark(X520))) [2] mark(U32(U31(X1360, X2360))) -> a__U32(a__U31(mark(X1360), X2360)) [2] mark(U32(U32(X521))) -> a__U32(a__U32(mark(X521))) [2] mark(U32(U41(X1361, X2361))) -> a__U32(a__U41(mark(X1361), X2361)) [2] mark(U32(U51(X1362, X2362, X3180))) -> a__U32(a__U51(mark(X1362), X2362, X3180)) [2] mark(U32(U52(X1363, X2363, X3181))) -> a__U32(a__U52(mark(X1363), X2363, X3181)) [2] mark(U32(plus(X1364, X2364))) -> a__U32(a__plus(mark(X1364), mark(X2364))) [2] mark(U32(U61(X522))) -> a__U32(a__U61(mark(X522))) [2] mark(U32(U71(X1365, X2365, X3182))) -> a__U32(a__U71(mark(X1365), X2365, X3182)) [2] mark(U32(U72(X1366, X2366, X3183))) -> a__U32(a__U72(mark(X1366), X2366, X3183)) [2] mark(U32(x(X1367, X2367))) -> a__U32(a__x(mark(X1367), mark(X2367))) [2] mark(U32(tt)) -> a__U32(tt) [2] mark(U32(s(X523))) -> a__U32(s(mark(X523))) [2] mark(U32(0)) -> a__U32(0) [2] mark(U41(U11(X1368, X2368), X2)) -> a__U41(a__U11(mark(X1368), X2368), X2) [2] mark(U41(U12(X524), X2)) -> a__U41(a__U12(mark(X524)), X2) [2] mark(U41(isNat(X525), X2)) -> a__U41(a__isNat(X525), X2) [2] mark(U41(U21(X526), X2)) -> a__U41(a__U21(mark(X526)), X2) [2] mark(U41(U31(X1369, X2369), X2)) -> a__U41(a__U31(mark(X1369), X2369), X2) [2] mark(U41(U32(X527), X2)) -> a__U41(a__U32(mark(X527)), X2) [2] mark(U41(U41(X1370, X2370), X2)) -> a__U41(a__U41(mark(X1370), X2370), X2) [2] mark(U41(U51(X1371, X2371, X3184), X2)) -> a__U41(a__U51(mark(X1371), X2371, X3184), X2) [2] mark(U41(U52(X1372, X2372, X3185), X2)) -> a__U41(a__U52(mark(X1372), X2372, X3185), X2) [2] mark(U41(plus(X1373, X2373), X2)) -> a__U41(a__plus(mark(X1373), mark(X2373)), X2) [2] mark(U41(U61(X528), X2)) -> a__U41(a__U61(mark(X528)), X2) [2] mark(U41(U71(X1374, X2374, X3186), X2)) -> a__U41(a__U71(mark(X1374), X2374, X3186), X2) [2] mark(U41(U72(X1375, X2375, X3187), X2)) -> a__U41(a__U72(mark(X1375), X2375, X3187), X2) [2] mark(U41(x(X1376, X2376), X2)) -> a__U41(a__x(mark(X1376), mark(X2376)), X2) [2] mark(U41(tt, X2)) -> a__U41(tt, X2) [2] mark(U41(s(X529), X2)) -> a__U41(s(mark(X529)), X2) [2] mark(U41(0, X2)) -> a__U41(0, X2) [2] mark(U51(U11(X1377, X2377), X2, X3)) -> a__U51(a__U11(mark(X1377), X2377), X2, X3) [2] mark(U51(U12(X530), X2, X3)) -> a__U51(a__U12(mark(X530)), X2, X3) [2] mark(U51(isNat(X531), X2, X3)) -> a__U51(a__isNat(X531), X2, X3) [2] mark(U51(U21(X532), X2, X3)) -> a__U51(a__U21(mark(X532)), X2, X3) [2] mark(U51(U31(X1378, X2378), X2, X3)) -> a__U51(a__U31(mark(X1378), X2378), X2, X3) [2] mark(U51(U32(X533), X2, X3)) -> a__U51(a__U32(mark(X533)), X2, X3) [2] mark(U51(U41(X1379, X2379), X2, X3)) -> a__U51(a__U41(mark(X1379), X2379), X2, X3) [2] mark(U51(U51(X1380, X2380, X3188), X2, X3)) -> a__U51(a__U51(mark(X1380), X2380, X3188), X2, X3) [2] mark(U51(U52(X1381, X2381, X3189), X2, X3)) -> a__U51(a__U52(mark(X1381), X2381, X3189), X2, X3) [2] mark(U51(plus(X1382, X2382), X2, X3)) -> a__U51(a__plus(mark(X1382), mark(X2382)), X2, X3) [2] mark(U51(U61(X534), X2, X3)) -> a__U51(a__U61(mark(X534)), X2, X3) [2] mark(U51(U71(X1383, X2383, X3190), X2, X3)) -> a__U51(a__U71(mark(X1383), X2383, X3190), X2, X3) [2] mark(U51(U72(X1384, X2384, X3191), X2, X3)) -> a__U51(a__U72(mark(X1384), X2384, X3191), X2, X3) [2] mark(U51(x(X1385, X2385), X2, X3)) -> a__U51(a__x(mark(X1385), mark(X2385)), X2, X3) [2] mark(U51(tt, X2, X3)) -> a__U51(tt, X2, X3) [2] mark(U51(s(X535), X2, X3)) -> a__U51(s(mark(X535)), X2, X3) [2] mark(U51(0, X2, X3)) -> a__U51(0, X2, X3) [2] mark(U52(U11(X1386, X2386), X2, X3)) -> a__U52(a__U11(mark(X1386), X2386), X2, X3) [2] mark(U52(U12(X536), X2, X3)) -> a__U52(a__U12(mark(X536)), X2, X3) [2] mark(U52(isNat(X537), X2, X3)) -> a__U52(a__isNat(X537), X2, X3) [2] mark(U52(U21(X538), X2, X3)) -> a__U52(a__U21(mark(X538)), X2, X3) [2] mark(U52(U31(X1387, X2387), X2, X3)) -> a__U52(a__U31(mark(X1387), X2387), X2, X3) [2] mark(U52(U32(X539), X2, X3)) -> a__U52(a__U32(mark(X539)), X2, X3) [2] mark(U52(U41(X1388, X2388), X2, X3)) -> a__U52(a__U41(mark(X1388), X2388), X2, X3) [2] mark(U52(U51(X1389, X2389, X3192), X2, X3)) -> a__U52(a__U51(mark(X1389), X2389, X3192), X2, X3) [2] mark(U52(U52(X1390, X2390, X3193), X2, X3)) -> a__U52(a__U52(mark(X1390), X2390, X3193), X2, X3) [2] mark(U52(plus(X1391, X2391), X2, X3)) -> a__U52(a__plus(mark(X1391), mark(X2391)), X2, X3) [2] mark(U52(U61(X540), X2, X3)) -> a__U52(a__U61(mark(X540)), X2, X3) [2] mark(U52(U71(X1392, X2392, X3194), X2, X3)) -> a__U52(a__U71(mark(X1392), X2392, X3194), X2, X3) [2] mark(U52(U72(X1393, X2393, X3195), X2, X3)) -> a__U52(a__U72(mark(X1393), X2393, X3195), X2, X3) [2] mark(U52(x(X1394, X2394), X2, X3)) -> a__U52(a__x(mark(X1394), mark(X2394)), X2, X3) [2] mark(U52(tt, X2, X3)) -> a__U52(tt, X2, X3) [2] mark(U52(s(X541), X2, X3)) -> a__U52(s(mark(X541)), X2, X3) [2] mark(U52(0, X2, X3)) -> a__U52(0, X2, X3) [2] mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) [1] mark(U61(U11(X1557, X2557))) -> a__U61(a__U11(mark(X1557), X2557)) [2] mark(U61(U12(X650))) -> a__U61(a__U12(mark(X650))) [2] mark(U61(isNat(X651))) -> a__U61(a__isNat(X651)) [2] mark(U61(U21(X652))) -> a__U61(a__U21(mark(X652))) [2] mark(U61(U31(X1558, X2558))) -> a__U61(a__U31(mark(X1558), X2558)) [2] mark(U61(U32(X653))) -> a__U61(a__U32(mark(X653))) [2] mark(U61(U41(X1559, X2559))) -> a__U61(a__U41(mark(X1559), X2559)) [2] mark(U61(U51(X1560, X2560, X3268))) -> a__U61(a__U51(mark(X1560), X2560, X3268)) [2] mark(U61(U52(X1561, X2561, X3269))) -> a__U61(a__U52(mark(X1561), X2561, X3269)) [2] mark(U61(plus(X1562, X2562))) -> a__U61(a__plus(mark(X1562), mark(X2562))) [2] mark(U61(U61(X654))) -> a__U61(a__U61(mark(X654))) [2] mark(U61(U71(X1563, X2563, X3270))) -> a__U61(a__U71(mark(X1563), X2563, X3270)) [2] mark(U61(U72(X1564, X2564, X3271))) -> a__U61(a__U72(mark(X1564), X2564, X3271)) [2] mark(U61(x(X1565, X2565))) -> a__U61(a__x(mark(X1565), mark(X2565))) [2] mark(U61(tt)) -> a__U61(tt) [2] mark(U61(s(X655))) -> a__U61(s(mark(X655))) [2] mark(U61(0)) -> a__U61(0) [2] mark(U71(U11(X1566, X2566), X2, X3)) -> a__U71(a__U11(mark(X1566), X2566), X2, X3) [2] mark(U71(U12(X656), X2, X3)) -> a__U71(a__U12(mark(X656)), X2, X3) [2] mark(U71(isNat(X657), X2, X3)) -> a__U71(a__isNat(X657), X2, X3) [2] mark(U71(U21(X658), X2, X3)) -> a__U71(a__U21(mark(X658)), X2, X3) [2] mark(U71(U31(X1567, X2567), X2, X3)) -> a__U71(a__U31(mark(X1567), X2567), X2, X3) [2] mark(U71(U32(X659), X2, X3)) -> a__U71(a__U32(mark(X659)), X2, X3) [2] mark(U71(U41(X1568, X2568), X2, X3)) -> a__U71(a__U41(mark(X1568), X2568), X2, X3) [2] mark(U71(U51(X1569, X2569, X3272), X2, X3)) -> a__U71(a__U51(mark(X1569), X2569, X3272), X2, X3) [2] mark(U71(U52(X1570, X2570, X3273), X2, X3)) -> a__U71(a__U52(mark(X1570), X2570, X3273), X2, X3) [2] mark(U71(plus(X1571, X2571), X2, X3)) -> a__U71(a__plus(mark(X1571), mark(X2571)), X2, X3) [2] mark(U71(U61(X660), X2, X3)) -> a__U71(a__U61(mark(X660)), X2, X3) [2] mark(U71(U71(X1572, X2572, X3274), X2, X3)) -> a__U71(a__U71(mark(X1572), X2572, X3274), X2, X3) [2] mark(U71(U72(X1573, X2573, X3275), X2, X3)) -> a__U71(a__U72(mark(X1573), X2573, X3275), X2, X3) [2] mark(U71(x(X1574, X2574), X2, X3)) -> a__U71(a__x(mark(X1574), mark(X2574)), X2, X3) [2] mark(U71(tt, X2, X3)) -> a__U71(tt, X2, X3) [2] mark(U71(s(X661), X2, X3)) -> a__U71(s(mark(X661)), X2, X3) [2] mark(U71(0, X2, X3)) -> a__U71(0, X2, X3) [2] mark(U72(U11(X1575, X2575), X2, X3)) -> a__U72(a__U11(mark(X1575), X2575), X2, X3) [2] mark(U72(U12(X662), X2, X3)) -> a__U72(a__U12(mark(X662)), X2, X3) [2] mark(U72(isNat(X663), X2, X3)) -> a__U72(a__isNat(X663), X2, X3) [2] mark(U72(U21(X664), X2, X3)) -> a__U72(a__U21(mark(X664)), X2, X3) [2] mark(U72(U31(X1576, X2576), X2, X3)) -> a__U72(a__U31(mark(X1576), X2576), X2, X3) [2] mark(U72(U32(X665), X2, X3)) -> a__U72(a__U32(mark(X665)), X2, X3) [2] mark(U72(U41(X1577, X2577), X2, X3)) -> a__U72(a__U41(mark(X1577), X2577), X2, X3) [2] mark(U72(U51(X1578, X2578, X3276), X2, X3)) -> a__U72(a__U51(mark(X1578), X2578, X3276), X2, X3) [2] mark(U72(U52(X1579, X2579, X3277), X2, X3)) -> a__U72(a__U52(mark(X1579), X2579, X3277), X2, X3) [2] mark(U72(plus(X1580, X2580), X2, X3)) -> a__U72(a__plus(mark(X1580), mark(X2580)), X2, X3) [2] mark(U72(U61(X666), X2, X3)) -> a__U72(a__U61(mark(X666)), X2, X3) [2] mark(U72(U71(X1581, X2581, X3278), X2, X3)) -> a__U72(a__U71(mark(X1581), X2581, X3278), X2, X3) [2] mark(U72(U72(X1582, X2582, X3279), X2, X3)) -> a__U72(a__U72(mark(X1582), X2582, X3279), X2, X3) [2] mark(U72(x(X1583, X2583), X2, X3)) -> a__U72(a__x(mark(X1583), mark(X2583)), X2, X3) [2] mark(U72(tt, X2, X3)) -> a__U72(tt, X2, X3) [2] mark(U72(s(X667), X2, X3)) -> a__U72(s(mark(X667)), X2, X3) [2] mark(U72(0, X2, X3)) -> a__U72(0, X2, X3) [2] mark(x(X1, X2)) -> a__x(mark(X1), mark(X2)) [1] mark(tt) -> tt [1] mark(s(X)) -> s(mark(X)) [1] mark(0) -> 0 [1] a__U11(X1, X2) -> U11(X1, X2) [1] a__U12(X) -> U12(X) [1] a__isNat(X) -> isNat(X) [1] a__U21(X) -> U21(X) [1] a__U31(X1, X2) -> U31(X1, X2) [1] a__U32(X) -> U32(X) [1] a__U41(X1, X2) -> U41(X1, X2) [1] a__U51(X1, X2, X3) -> U51(X1, X2, X3) [1] a__U52(X1, X2, X3) -> U52(X1, X2, X3) [1] a__plus(X1, X2) -> plus(X1, X2) [1] a__U61(X) -> U61(X) [1] a__U71(X1, X2, X3) -> U71(X1, X2, X3) [1] a__U72(X1, X2, X3) -> U72(X1, X2, X3) [1] a__x(X1, X2) -> x(X1, X2) [1] The TRS has the following type information: a__U11 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 tt :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U12 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__isNat :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U21 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U31 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U32 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U41 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 mark :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U51 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U52 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 s :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__plus :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U61 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 0 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U71 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__U72 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 a__x :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 plus :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 x :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 U11 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 U12 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 isNat :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 U21 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 U31 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 U32 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 U41 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 U51 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 U52 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 U61 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 U71 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 U72 :: tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 -> tt:s:0:plus:x:U11:U12:isNat:U21:U31:U32:U41:U51:U52:U61:U71:U72 Rewrite Strategy: INNERMOST ---------------------------------------- (31) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: tt => 1 0 => 0 ---------------------------------------- (32) Obligation: Complexity RNTS consisting of the following rules: a__U11(z, z') -{ 2 }-> a__U12(a__U31(a__isNat(V11), V2'')) :|: V11 >= 0, V2'' >= 0, z = 1, z' = 1 + V11 + V2'' a__U11(z, z') -{ 2 }-> a__U12(a__U21(a__isNat(V1''))) :|: V1'' >= 0, z = 1, z' = 1 + V1'' a__U11(z, z') -{ 2 }-> a__U12(a__U11(a__isNat(V1'), V2')) :|: z = 1, z' = 1 + V1' + V2', V2' >= 0, V1' >= 0 a__U11(z, z') -{ 2 }-> a__U12(1) :|: z = 1, z' = 0 a__U11(z, z') -{ 2 }-> a__U12(1 + V2) :|: z' = V2, z = 1, V2 >= 0 a__U11(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U12(z) -{ 1 }-> 1 :|: z = 1 a__U12(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U21(z) -{ 1 }-> 1 :|: z = 1 a__U21(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U31(z, z') -{ 2 }-> a__U32(a__U31(a__isNat(V14), V22)) :|: V14 >= 0, z' = 1 + V14 + V22, z = 1, V22 >= 0 a__U31(z, z') -{ 2 }-> a__U32(a__U21(a__isNat(V13))) :|: V13 >= 0, z = 1, z' = 1 + V13 a__U31(z, z') -{ 2 }-> a__U32(a__U11(a__isNat(V12), V21)) :|: V21 >= 0, z' = 1 + V12 + V21, z = 1, V12 >= 0 a__U31(z, z') -{ 2 }-> a__U32(1) :|: z = 1, z' = 0 a__U31(z, z') -{ 2 }-> a__U32(1 + V2) :|: z' = V2, z = 1, V2 >= 0 a__U31(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U32(z) -{ 1 }-> 1 :|: z = 1 a__U32(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U41(z, z') -{ 1 }-> mark(N) :|: z = 1, z' = N, N >= 0 a__U41(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U51(z, z', z'') -{ 2 }-> a__U52(a__U31(a__isNat(V17), V24), M, 1 + V17 + V24) :|: z' = M, V24 >= 0, z = 1, z'' = 1 + V17 + V24, M >= 0, V17 >= 0 a__U51(z, z', z'') -{ 2 }-> a__U52(a__U21(a__isNat(V16)), M, 1 + V16) :|: z' = M, z'' = 1 + V16, z = 1, V16 >= 0, M >= 0 a__U51(z, z', z'') -{ 2 }-> a__U52(a__U11(a__isNat(V15), V23), M, 1 + V15 + V23) :|: z' = M, z = 1, V23 >= 0, z'' = 1 + V15 + V23, V15 >= 0, M >= 0 a__U51(z, z', z'') -{ 2 }-> a__U52(1, M, 0) :|: z'' = 0, z' = M, z = 1, M >= 0 a__U51(z, z', z'') -{ 2 }-> a__U52(1 + N, M, N) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0 a__U51(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U52(z, z', z'') -{ 1 }-> 1 + a__plus(mark(N), mark(M)) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0 a__U52(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U61(z) -{ 1 }-> 0 :|: z = 1 a__U61(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U71(z, z', z'') -{ 2 }-> a__U72(a__U31(a__isNat(V110), V26), M, 1 + V110 + V26) :|: V110 >= 0, z' = M, z = 1, z'' = 1 + V110 + V26, M >= 0, V26 >= 0 a__U71(z, z', z'') -{ 2 }-> a__U72(a__U21(a__isNat(V19)), M, 1 + V19) :|: z' = M, z = 1, V19 >= 0, z'' = 1 + V19, M >= 0 a__U71(z, z', z'') -{ 2 }-> a__U72(a__U11(a__isNat(V18), V25), M, 1 + V18 + V25) :|: z' = M, V25 >= 0, V18 >= 0, z = 1, z'' = 1 + V18 + V25, M >= 0 a__U71(z, z', z'') -{ 2 }-> a__U72(1, M, 0) :|: z'' = 0, z' = M, z = 1, M >= 0 a__U71(z, z', z'') -{ 2 }-> a__U72(1 + N, M, N) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0 a__U71(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U72(z, z', z'') -{ 1 }-> a__plus(a__x(mark(N), mark(M)), mark(N)) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0 a__U72(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__isNat(z) -{ 2 }-> a__U31(a__U31(a__isNat(V119), V212), V2) :|: z = 1 + (1 + V119 + V212) + V2, V2 >= 0, V119 >= 0, V212 >= 0 a__isNat(z) -{ 2 }-> a__U31(a__U21(a__isNat(V118)), V2) :|: V118 >= 0, z = 1 + (1 + V118) + V2, V2 >= 0 a__isNat(z) -{ 2 }-> a__U31(a__U11(a__isNat(V117), V211), V2) :|: z = 1 + (1 + V117 + V211) + V2, V117 >= 0, V2 >= 0, V211 >= 0 a__isNat(z) -{ 2 }-> a__U31(1, V2) :|: V2 >= 0, z = 1 + 0 + V2 a__isNat(z) -{ 2 }-> a__U31(1 + V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNat(z) -{ 2 }-> a__U21(a__U31(a__isNat(V116), V210)) :|: V116 >= 0, V210 >= 0, z = 1 + (1 + V116 + V210) a__isNat(z) -{ 2 }-> a__U21(a__U21(a__isNat(V115))) :|: z = 1 + (1 + V115), V115 >= 0 a__isNat(z) -{ 2 }-> a__U21(a__U11(a__isNat(V114), V29)) :|: V114 >= 0, V29 >= 0, z = 1 + (1 + V114 + V29) a__isNat(z) -{ 2 }-> a__U21(1) :|: z = 1 + 0 a__isNat(z) -{ 2 }-> a__U21(1 + V1) :|: z = 1 + V1, V1 >= 0 a__isNat(z) -{ 2 }-> a__U11(a__U31(a__isNat(V113), V28), V2) :|: V28 >= 0, V2 >= 0, z = 1 + (1 + V113 + V28) + V2, V113 >= 0 a__isNat(z) -{ 2 }-> a__U11(a__U21(a__isNat(V112)), V2) :|: z = 1 + (1 + V112) + V2, V2 >= 0, V112 >= 0 a__isNat(z) -{ 2 }-> a__U11(a__U11(a__isNat(V111), V27), V2) :|: z = 1 + (1 + V111 + V27) + V2, V2 >= 0, V111 >= 0, V27 >= 0 a__isNat(z) -{ 2 }-> a__U11(1, V2) :|: V2 >= 0, z = 1 + 0 + V2 a__isNat(z) -{ 2 }-> a__U11(1 + V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNat(z) -{ 1 }-> 1 :|: z = 0 a__isNat(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__plus(z, z') -{ 2 }-> a__U51(a__U31(a__isNat(V125), V216), 1 + V125 + V216, N) :|: z' = 1 + (1 + V125 + V216), V125 >= 0, z = N, V216 >= 0, N >= 0 a__plus(z, z') -{ 2 }-> a__U51(a__U21(a__isNat(V124)), 1 + V124, N) :|: V124 >= 0, z = N, z' = 1 + (1 + V124), N >= 0 a__plus(z, z') -{ 2 }-> a__U51(a__U11(a__isNat(V123), V215), 1 + V123 + V215, N) :|: z' = 1 + (1 + V123 + V215), z = N, V215 >= 0, N >= 0, V123 >= 0 a__plus(z, z') -{ 2 }-> a__U51(1, 0, N) :|: z = N, z' = 1 + 0, N >= 0 a__plus(z, z') -{ 2 }-> a__U51(1 + M, M, N) :|: z' = 1 + M, z = N, M >= 0, N >= 0 a__plus(z, z') -{ 2 }-> a__U41(a__U31(a__isNat(V122), V214), 1 + V122 + V214) :|: V122 >= 0, V214 >= 0, z = 1 + V122 + V214, z' = 0 a__plus(z, z') -{ 2 }-> a__U41(a__U21(a__isNat(V121)), 1 + V121) :|: z = 1 + V121, V121 >= 0, z' = 0 a__plus(z, z') -{ 2 }-> a__U41(a__U11(a__isNat(V120), V213), 1 + V120 + V213) :|: V120 >= 0, V213 >= 0, z = 1 + V120 + V213, z' = 0 a__plus(z, z') -{ 2 }-> a__U41(1, 0) :|: z = 0, z' = 0 a__plus(z, z') -{ 2 }-> a__U41(1 + N, N) :|: z = N, z' = 0, N >= 0 a__plus(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__x(z, z') -{ 2 }-> a__U71(a__U31(a__isNat(V131), V220), 1 + V131 + V220, N) :|: V131 >= 0, V220 >= 0, z = N, z' = 1 + (1 + V131 + V220), N >= 0 a__x(z, z') -{ 2 }-> a__U71(a__U21(a__isNat(V130)), 1 + V130, N) :|: V130 >= 0, z = N, z' = 1 + (1 + V130), N >= 0 a__x(z, z') -{ 2 }-> a__U71(a__U11(a__isNat(V129), V219), 1 + V129 + V219, N) :|: z = N, z' = 1 + (1 + V129 + V219), V129 >= 0, V219 >= 0, N >= 0 a__x(z, z') -{ 2 }-> a__U71(1, 0, N) :|: z = N, z' = 1 + 0, N >= 0 a__x(z, z') -{ 2 }-> a__U71(1 + M, M, N) :|: z' = 1 + M, z = N, M >= 0, N >= 0 a__x(z, z') -{ 2 }-> a__U61(a__U31(a__isNat(V128), V218)) :|: z = 1 + V128 + V218, V128 >= 0, V218 >= 0, z' = 0 a__x(z, z') -{ 2 }-> a__U61(a__U21(a__isNat(V127))) :|: z = 1 + V127, V127 >= 0, z' = 0 a__x(z, z') -{ 2 }-> a__U61(a__U11(a__isNat(V126), V217)) :|: V217 >= 0, V126 >= 0, z = 1 + V126 + V217, z' = 0 a__x(z, z') -{ 2 }-> a__U61(1) :|: z = 0, z' = 0 a__x(z, z') -{ 2 }-> a__U61(1 + N) :|: z = N, z' = 0, N >= 0 a__x(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 mark(z) -{ 1 }-> a__x(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__plus(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__isNat(X) :|: z = 1 + X, X >= 0 mark(z) -{ 2 }-> a__U72(a__x(mark(X1583), mark(X2583)), X2, X3) :|: X1583 >= 0, X2583 >= 0, X3 >= 0, z = 1 + (1 + X1583 + X2583) + X2 + X3, X2 >= 0 mark(z) -{ 2 }-> a__U72(a__plus(mark(X1580), mark(X2580)), X2, X3) :|: X1580 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X1580 + X2580) + X2 + X3, X2580 >= 0 mark(z) -{ 2 }-> a__U72(a__isNat(X663), X2, X3) :|: z = 1 + (1 + X663) + X2 + X3, X3 >= 0, X2 >= 0, X663 >= 0 mark(z) -{ 2 }-> a__U72(a__U72(mark(X1582), X2582, X3279), X2, X3) :|: X2582 >= 0, X3 >= 0, X1582 >= 0, X3279 >= 0, z = 1 + (1 + X1582 + X2582 + X3279) + X2 + X3, X2 >= 0 mark(z) -{ 2 }-> a__U72(a__U71(mark(X1581), X2581, X3278), X2, X3) :|: X1581 >= 0, X3 >= 0, X3278 >= 0, X2 >= 0, z = 1 + (1 + X1581 + X2581 + X3278) + X2 + X3, X2581 >= 0 mark(z) -{ 2 }-> a__U72(a__U61(mark(X666)), X2, X3) :|: z = 1 + (1 + X666) + X2 + X3, X666 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U72(a__U52(mark(X1579), X2579, X3277), X2, X3) :|: X2579 >= 0, X1579 >= 0, X3 >= 0, z = 1 + (1 + X1579 + X2579 + X3277) + X2 + X3, X2 >= 0, X3277 >= 0 mark(z) -{ 2 }-> a__U72(a__U51(mark(X1578), X2578, X3276), X2, X3) :|: z = 1 + (1 + X1578 + X2578 + X3276) + X2 + X3, X1578 >= 0, X3 >= 0, X2 >= 0, X3276 >= 0, X2578 >= 0 mark(z) -{ 2 }-> a__U72(a__U41(mark(X1577), X2577), X2, X3) :|: X1577 >= 0, X3 >= 0, X2577 >= 0, X2 >= 0, z = 1 + (1 + X1577 + X2577) + X2 + X3 mark(z) -{ 2 }-> a__U72(a__U32(mark(X665)), X2, X3) :|: X665 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X665) + X2 + X3 mark(z) -{ 2 }-> a__U72(a__U31(mark(X1576), X2576), X2, X3) :|: z = 1 + (1 + X1576 + X2576) + X2 + X3, X2576 >= 0, X3 >= 0, X2 >= 0, X1576 >= 0 mark(z) -{ 2 }-> a__U72(a__U21(mark(X664)), X2, X3) :|: X664 >= 0, z = 1 + (1 + X664) + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U72(a__U12(mark(X662)), X2, X3) :|: z = 1 + (1 + X662) + X2 + X3, X3 >= 0, X2 >= 0, X662 >= 0 mark(z) -{ 2 }-> a__U72(a__U11(mark(X1575), X2575), X2, X3) :|: X2575 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X1575 + X2575) + X2 + X3, X1575 >= 0 mark(z) -{ 2 }-> a__U72(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U72(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U72(1 + mark(X667), X2, X3) :|: z = 1 + (1 + X667) + X2 + X3, X667 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U71(a__x(mark(X1574), mark(X2574)), X2, X3) :|: X2574 >= 0, X3 >= 0, z = 1 + (1 + X1574 + X2574) + X2 + X3, X2 >= 0, X1574 >= 0 mark(z) -{ 2 }-> a__U71(a__plus(mark(X1571), mark(X2571)), X2, X3) :|: X2571 >= 0, z = 1 + (1 + X1571 + X2571) + X2 + X3, X1571 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U71(a__isNat(X657), X2, X3) :|: z = 1 + (1 + X657) + X2 + X3, X657 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U71(a__U72(mark(X1573), X2573, X3275), X2, X3) :|: X1573 >= 0, X3 >= 0, X2573 >= 0, z = 1 + (1 + X1573 + X2573 + X3275) + X2 + X3, X3275 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U71(a__U71(mark(X1572), X2572, X3274), X2, X3) :|: z = 1 + (1 + X1572 + X2572 + X3274) + X2 + X3, X2572 >= 0, X1572 >= 0, X3 >= 0, X3274 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U71(a__U61(mark(X660)), X2, X3) :|: z = 1 + (1 + X660) + X2 + X3, X660 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U71(a__U52(mark(X1570), X2570, X3273), X2, X3) :|: z = 1 + (1 + X1570 + X2570 + X3273) + X2 + X3, X1570 >= 0, X3273 >= 0, X3 >= 0, X2 >= 0, X2570 >= 0 mark(z) -{ 2 }-> a__U71(a__U51(mark(X1569), X2569, X3272), X2, X3) :|: X2569 >= 0, X3272 >= 0, X1569 >= 0, X3 >= 0, z = 1 + (1 + X1569 + X2569 + X3272) + X2 + X3, X2 >= 0 mark(z) -{ 2 }-> a__U71(a__U41(mark(X1568), X2568), X2, X3) :|: X1568 >= 0, z = 1 + (1 + X1568 + X2568) + X2 + X3, X3 >= 0, X2 >= 0, X2568 >= 0 mark(z) -{ 2 }-> a__U71(a__U32(mark(X659)), X2, X3) :|: z = 1 + (1 + X659) + X2 + X3, X3 >= 0, X659 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U71(a__U31(mark(X1567), X2567), X2, X3) :|: z = 1 + (1 + X1567 + X2567) + X2 + X3, X1567 >= 0, X3 >= 0, X2567 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U71(a__U21(mark(X658)), X2, X3) :|: X658 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X658) + X2 + X3 mark(z) -{ 2 }-> a__U71(a__U12(mark(X656)), X2, X3) :|: z = 1 + (1 + X656) + X2 + X3, X656 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U71(a__U11(mark(X1566), X2566), X2, X3) :|: X3 >= 0, z = 1 + (1 + X1566 + X2566) + X2 + X3, X2566 >= 0, X2 >= 0, X1566 >= 0 mark(z) -{ 2 }-> a__U71(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U71(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U71(1 + mark(X661), X2, X3) :|: z = 1 + (1 + X661) + X2 + X3, X661 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U61(a__x(mark(X1565), mark(X2565))) :|: X2565 >= 0, z = 1 + (1 + X1565 + X2565), X1565 >= 0 mark(z) -{ 2 }-> a__U61(a__plus(mark(X1562), mark(X2562))) :|: z = 1 + (1 + X1562 + X2562), X1562 >= 0, X2562 >= 0 mark(z) -{ 2 }-> a__U61(a__isNat(X651)) :|: X651 >= 0, z = 1 + (1 + X651) mark(z) -{ 2 }-> a__U61(a__U72(mark(X1564), X2564, X3271)) :|: X2564 >= 0, X3271 >= 0, X1564 >= 0, z = 1 + (1 + X1564 + X2564 + X3271) mark(z) -{ 2 }-> a__U61(a__U71(mark(X1563), X2563, X3270)) :|: X1563 >= 0, z = 1 + (1 + X1563 + X2563 + X3270), X2563 >= 0, X3270 >= 0 mark(z) -{ 2 }-> a__U61(a__U61(mark(X654))) :|: X654 >= 0, z = 1 + (1 + X654) mark(z) -{ 2 }-> a__U61(a__U52(mark(X1561), X2561, X3269)) :|: X2561 >= 0, X3269 >= 0, X1561 >= 0, z = 1 + (1 + X1561 + X2561 + X3269) mark(z) -{ 2 }-> a__U61(a__U51(mark(X1560), X2560, X3268)) :|: X1560 >= 0, z = 1 + (1 + X1560 + X2560 + X3268), X3268 >= 0, X2560 >= 0 mark(z) -{ 2 }-> a__U61(a__U41(mark(X1559), X2559)) :|: z = 1 + (1 + X1559 + X2559), X1559 >= 0, X2559 >= 0 mark(z) -{ 2 }-> a__U61(a__U32(mark(X653))) :|: z = 1 + (1 + X653), X653 >= 0 mark(z) -{ 2 }-> a__U61(a__U31(mark(X1558), X2558)) :|: X1558 >= 0, z = 1 + (1 + X1558 + X2558), X2558 >= 0 mark(z) -{ 2 }-> a__U61(a__U21(mark(X652))) :|: X652 >= 0, z = 1 + (1 + X652) mark(z) -{ 2 }-> a__U61(a__U12(mark(X650))) :|: X650 >= 0, z = 1 + (1 + X650) mark(z) -{ 2 }-> a__U61(a__U11(mark(X1557), X2557)) :|: z = 1 + (1 + X1557 + X2557), X1557 >= 0, X2557 >= 0 mark(z) -{ 2 }-> a__U61(1) :|: z = 1 + 1 mark(z) -{ 2 }-> a__U61(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__U61(1 + mark(X655)) :|: X655 >= 0, z = 1 + (1 + X655) mark(z) -{ 2 }-> a__U52(a__x(mark(X1394), mark(X2394)), X2, X3) :|: X2394 >= 0, z = 1 + (1 + X1394 + X2394) + X2 + X3, X1394 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U52(a__plus(mark(X1391), mark(X2391)), X2, X3) :|: X2391 >= 0, z = 1 + (1 + X1391 + X2391) + X2 + X3, X3 >= 0, X1391 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U52(a__isNat(X537), X2, X3) :|: z = 1 + (1 + X537) + X2 + X3, X537 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U52(a__U72(mark(X1393), X2393, X3195), X2, X3) :|: z = 1 + (1 + X1393 + X2393 + X3195) + X2 + X3, X3195 >= 0, X1393 >= 0, X3 >= 0, X2 >= 0, X2393 >= 0 mark(z) -{ 2 }-> a__U52(a__U71(mark(X1392), X2392, X3194), X2, X3) :|: X1392 >= 0, X3194 >= 0, X3 >= 0, z = 1 + (1 + X1392 + X2392 + X3194) + X2 + X3, X2 >= 0, X2392 >= 0 mark(z) -{ 2 }-> a__U52(a__U61(mark(X540)), X2, X3) :|: z = 1 + (1 + X540) + X2 + X3, X540 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U52(a__U52(mark(X1390), X2390, X3193), X2, X3) :|: X2390 >= 0, z = 1 + (1 + X1390 + X2390 + X3193) + X2 + X3, X3 >= 0, X3193 >= 0, X2 >= 0, X1390 >= 0 mark(z) -{ 2 }-> a__U52(a__U51(mark(X1389), X2389, X3192), X2, X3) :|: X3 >= 0, z = 1 + (1 + X1389 + X2389 + X3192) + X2 + X3, X3192 >= 0, X1389 >= 0, X2389 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U52(a__U41(mark(X1388), X2388), X2, X3) :|: X2388 >= 0, z = 1 + (1 + X1388 + X2388) + X2 + X3, X1388 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U52(a__U32(mark(X539)), X2, X3) :|: z = 1 + (1 + X539) + X2 + X3, X539 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U52(a__U31(mark(X1387), X2387), X2, X3) :|: X2387 >= 0, X3 >= 0, X1387 >= 0, X2 >= 0, z = 1 + (1 + X1387 + X2387) + X2 + X3 mark(z) -{ 2 }-> a__U52(a__U21(mark(X538)), X2, X3) :|: z = 1 + (1 + X538) + X2 + X3, X538 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U52(a__U12(mark(X536)), X2, X3) :|: z = 1 + (1 + X536) + X2 + X3, X3 >= 0, X536 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U52(a__U11(mark(X1386), X2386), X2, X3) :|: X1386 >= 0, X2386 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X1386 + X2386) + X2 + X3 mark(z) -{ 2 }-> a__U52(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U52(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U52(1 + mark(X541), X2, X3) :|: z = 1 + (1 + X541) + X2 + X3, X541 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U51(a__x(mark(X1385), mark(X2385)), X2, X3) :|: X1385 >= 0, X2385 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X1385 + X2385) + X2 + X3 mark(z) -{ 2 }-> a__U51(a__plus(mark(X1382), mark(X2382)), X2, X3) :|: X1382 >= 0, z = 1 + (1 + X1382 + X2382) + X2 + X3, X2382 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U51(a__isNat(X531), X2, X3) :|: z = 1 + (1 + X531) + X2 + X3, X531 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U51(a__U72(mark(X1384), X2384, X3191), X2, X3) :|: X2384 >= 0, X3191 >= 0, z = 1 + (1 + X1384 + X2384 + X3191) + X2 + X3, X1384 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U51(a__U71(mark(X1383), X2383, X3190), X2, X3) :|: z = 1 + (1 + X1383 + X2383 + X3190) + X2 + X3, X1383 >= 0, X3 >= 0, X2383 >= 0, X2 >= 0, X3190 >= 0 mark(z) -{ 2 }-> a__U51(a__U61(mark(X534)), X2, X3) :|: X3 >= 0, X2 >= 0, z = 1 + (1 + X534) + X2 + X3, X534 >= 0 mark(z) -{ 2 }-> a__U51(a__U52(mark(X1381), X2381, X3189), X2, X3) :|: X3 >= 0, X1381 >= 0, X2381 >= 0, X3189 >= 0, X2 >= 0, z = 1 + (1 + X1381 + X2381 + X3189) + X2 + X3 mark(z) -{ 2 }-> a__U51(a__U51(mark(X1380), X2380, X3188), X2, X3) :|: X2380 >= 0, X3188 >= 0, X1380 >= 0, X3 >= 0, z = 1 + (1 + X1380 + X2380 + X3188) + X2 + X3, X2 >= 0 mark(z) -{ 2 }-> a__U51(a__U41(mark(X1379), X2379), X2, X3) :|: z = 1 + (1 + X1379 + X2379) + X2 + X3, X1379 >= 0, X3 >= 0, X2379 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U51(a__U32(mark(X533)), X2, X3) :|: X3 >= 0, z = 1 + (1 + X533) + X2 + X3, X2 >= 0, X533 >= 0 mark(z) -{ 2 }-> a__U51(a__U31(mark(X1378), X2378), X2, X3) :|: X2378 >= 0, z = 1 + (1 + X1378 + X2378) + X2 + X3, X3 >= 0, X2 >= 0, X1378 >= 0 mark(z) -{ 2 }-> a__U51(a__U21(mark(X532)), X2, X3) :|: z = 1 + (1 + X532) + X2 + X3, X3 >= 0, X532 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U51(a__U12(mark(X530)), X2, X3) :|: X530 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X530) + X2 + X3 mark(z) -{ 2 }-> a__U51(a__U11(mark(X1377), X2377), X2, X3) :|: X2377 >= 0, z = 1 + (1 + X1377 + X2377) + X2 + X3, X3 >= 0, X2 >= 0, X1377 >= 0 mark(z) -{ 2 }-> a__U51(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U51(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U51(1 + mark(X535), X2, X3) :|: X3 >= 0, z = 1 + (1 + X535) + X2 + X3, X2 >= 0, X535 >= 0 mark(z) -{ 2 }-> a__U41(a__x(mark(X1376), mark(X2376)), X2) :|: X1376 >= 0, X2376 >= 0, z = 1 + (1 + X1376 + X2376) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__plus(mark(X1373), mark(X2373)), X2) :|: z = 1 + (1 + X1373 + X2373) + X2, X1373 >= 0, X2 >= 0, X2373 >= 0 mark(z) -{ 2 }-> a__U41(a__isNat(X525), X2) :|: z = 1 + (1 + X525) + X2, X2 >= 0, X525 >= 0 mark(z) -{ 2 }-> a__U41(a__U72(mark(X1375), X2375, X3187), X2) :|: X1375 >= 0, z = 1 + (1 + X1375 + X2375 + X3187) + X2, X2375 >= 0, X3187 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U71(mark(X1374), X2374, X3186), X2) :|: X2374 >= 0, X1374 >= 0, z = 1 + (1 + X1374 + X2374 + X3186) + X2, X3186 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U61(mark(X528)), X2) :|: X528 >= 0, z = 1 + (1 + X528) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U52(mark(X1372), X2372, X3185), X2) :|: X1372 >= 0, X3185 >= 0, z = 1 + (1 + X1372 + X2372 + X3185) + X2, X2 >= 0, X2372 >= 0 mark(z) -{ 2 }-> a__U41(a__U51(mark(X1371), X2371, X3184), X2) :|: X1371 >= 0, z = 1 + (1 + X1371 + X2371 + X3184) + X2, X3184 >= 0, X2371 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U41(mark(X1370), X2370), X2) :|: X2370 >= 0, z = 1 + (1 + X1370 + X2370) + X2, X2 >= 0, X1370 >= 0 mark(z) -{ 2 }-> a__U41(a__U32(mark(X527)), X2) :|: X527 >= 0, X2 >= 0, z = 1 + (1 + X527) + X2 mark(z) -{ 2 }-> a__U41(a__U31(mark(X1369), X2369), X2) :|: X1369 >= 0, z = 1 + (1 + X1369 + X2369) + X2, X2369 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U21(mark(X526)), X2) :|: z = 1 + (1 + X526) + X2, X526 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U12(mark(X524)), X2) :|: X2 >= 0, z = 1 + (1 + X524) + X2, X524 >= 0 mark(z) -{ 2 }-> a__U41(a__U11(mark(X1368), X2368), X2) :|: X2368 >= 0, z = 1 + (1 + X1368 + X2368) + X2, X1368 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(1, X2) :|: z = 1 + 1 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U41(0, X2) :|: z = 1 + 0 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U41(1 + mark(X529), X2) :|: z = 1 + (1 + X529) + X2, X529 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U32(a__x(mark(X1367), mark(X2367))) :|: z = 1 + (1 + X1367 + X2367), X2367 >= 0, X1367 >= 0 mark(z) -{ 2 }-> a__U32(a__plus(mark(X1364), mark(X2364))) :|: X1364 >= 0, z = 1 + (1 + X1364 + X2364), X2364 >= 0 mark(z) -{ 2 }-> a__U32(a__isNat(X519)) :|: z = 1 + (1 + X519), X519 >= 0 mark(z) -{ 2 }-> a__U32(a__U72(mark(X1366), X2366, X3183)) :|: X2366 >= 0, X3183 >= 0, z = 1 + (1 + X1366 + X2366 + X3183), X1366 >= 0 mark(z) -{ 2 }-> a__U32(a__U71(mark(X1365), X2365, X3182)) :|: X1365 >= 0, X2365 >= 0, X3182 >= 0, z = 1 + (1 + X1365 + X2365 + X3182) mark(z) -{ 2 }-> a__U32(a__U61(mark(X522))) :|: z = 1 + (1 + X522), X522 >= 0 mark(z) -{ 2 }-> a__U32(a__U52(mark(X1363), X2363, X3181)) :|: X2363 >= 0, X1363 >= 0, X3181 >= 0, z = 1 + (1 + X1363 + X2363 + X3181) mark(z) -{ 2 }-> a__U32(a__U51(mark(X1362), X2362, X3180)) :|: X1362 >= 0, z = 1 + (1 + X1362 + X2362 + X3180), X2362 >= 0, X3180 >= 0 mark(z) -{ 2 }-> a__U32(a__U41(mark(X1361), X2361)) :|: X1361 >= 0, X2361 >= 0, z = 1 + (1 + X1361 + X2361) mark(z) -{ 2 }-> a__U32(a__U32(mark(X521))) :|: X521 >= 0, z = 1 + (1 + X521) mark(z) -{ 2 }-> a__U32(a__U31(mark(X1360), X2360)) :|: X2360 >= 0, X1360 >= 0, z = 1 + (1 + X1360 + X2360) mark(z) -{ 2 }-> a__U32(a__U21(mark(X520))) :|: z = 1 + (1 + X520), X520 >= 0 mark(z) -{ 2 }-> a__U32(a__U12(mark(X518))) :|: X518 >= 0, z = 1 + (1 + X518) mark(z) -{ 2 }-> a__U32(a__U11(mark(X1359), X2359)) :|: z = 1 + (1 + X1359 + X2359), X1359 >= 0, X2359 >= 0 mark(z) -{ 2 }-> a__U32(1) :|: z = 1 + 1 mark(z) -{ 2 }-> a__U32(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__U32(1 + mark(X523)) :|: z = 1 + (1 + X523), X523 >= 0 mark(z) -{ 2 }-> a__U31(a__x(mark(X1358), mark(X2358)), X2) :|: z = 1 + (1 + X1358 + X2358) + X2, X2358 >= 0, X2 >= 0, X1358 >= 0 mark(z) -{ 2 }-> a__U31(a__plus(mark(X1355), mark(X2355)), X2) :|: X1355 >= 0, z = 1 + (1 + X1355 + X2355) + X2, X2355 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__isNat(X513), X2) :|: X513 >= 0, X2 >= 0, z = 1 + (1 + X513) + X2 mark(z) -{ 2 }-> a__U31(a__U72(mark(X1357), X2357, X3179), X2) :|: z = 1 + (1 + X1357 + X2357 + X3179) + X2, X2357 >= 0, X3179 >= 0, X2 >= 0, X1357 >= 0 mark(z) -{ 2 }-> a__U31(a__U71(mark(X1356), X2356, X3178), X2) :|: X2356 >= 0, X1356 >= 0, X2 >= 0, X3178 >= 0, z = 1 + (1 + X1356 + X2356 + X3178) + X2 mark(z) -{ 2 }-> a__U31(a__U61(mark(X516)), X2) :|: z = 1 + (1 + X516) + X2, X516 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__U52(mark(X1354), X2354, X3177), X2) :|: X1354 >= 0, z = 1 + (1 + X1354 + X2354 + X3177) + X2, X2354 >= 0, X2 >= 0, X3177 >= 0 mark(z) -{ 2 }-> a__U31(a__U51(mark(X1353), X2353, X3176), X2) :|: X1353 >= 0, X3176 >= 0, X2 >= 0, z = 1 + (1 + X1353 + X2353 + X3176) + X2, X2353 >= 0 mark(z) -{ 2 }-> a__U31(a__U41(mark(X1352), X2352), X2) :|: z = 1 + (1 + X1352 + X2352) + X2, X1352 >= 0, X2 >= 0, X2352 >= 0 mark(z) -{ 2 }-> a__U31(a__U32(mark(X515)), X2) :|: z = 1 + (1 + X515) + X2, X515 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__U31(mark(X1351), X2351), X2) :|: X1351 >= 0, z = 1 + (1 + X1351 + X2351) + X2, X2351 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__U21(mark(X514)), X2) :|: z = 1 + (1 + X514) + X2, X2 >= 0, X514 >= 0 mark(z) -{ 2 }-> a__U31(a__U12(mark(X512)), X2) :|: z = 1 + (1 + X512) + X2, X512 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__U11(mark(X1350), X2350), X2) :|: z = 1 + (1 + X1350 + X2350) + X2, X2350 >= 0, X2 >= 0, X1350 >= 0 mark(z) -{ 2 }-> a__U31(1, X2) :|: z = 1 + 1 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U31(0, X2) :|: z = 1 + 0 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U31(1 + mark(X517), X2) :|: X517 >= 0, z = 1 + (1 + X517) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__x(mark(X1349), mark(X2349))) :|: z = 1 + (1 + X1349 + X2349), X1349 >= 0, X2349 >= 0 mark(z) -{ 2 }-> a__U21(a__plus(mark(X1346), mark(X2346))) :|: X2346 >= 0, X1346 >= 0, z = 1 + (1 + X1346 + X2346) mark(z) -{ 2 }-> a__U21(a__isNat(X507)) :|: X507 >= 0, z = 1 + (1 + X507) mark(z) -{ 2 }-> a__U21(a__U72(mark(X1348), X2348, X3175)) :|: X1348 >= 0, X3175 >= 0, X2348 >= 0, z = 1 + (1 + X1348 + X2348 + X3175) mark(z) -{ 2 }-> a__U21(a__U71(mark(X1347), X2347, X3174)) :|: z = 1 + (1 + X1347 + X2347 + X3174), X2347 >= 0, X3174 >= 0, X1347 >= 0 mark(z) -{ 2 }-> a__U21(a__U61(mark(X510))) :|: z = 1 + (1 + X510), X510 >= 0 mark(z) -{ 2 }-> a__U21(a__U52(mark(X1345), X2345, X3173)) :|: z = 1 + (1 + X1345 + X2345 + X3173), X1345 >= 0, X2345 >= 0, X3173 >= 0 mark(z) -{ 2 }-> a__U21(a__U51(mark(X1344), X2344, X3172)) :|: X1344 >= 0, z = 1 + (1 + X1344 + X2344 + X3172), X2344 >= 0, X3172 >= 0 mark(z) -{ 2 }-> a__U21(a__U41(mark(X1343), X2343)) :|: z = 1 + (1 + X1343 + X2343), X1343 >= 0, X2343 >= 0 mark(z) -{ 2 }-> a__U21(a__U32(mark(X509))) :|: X509 >= 0, z = 1 + (1 + X509) mark(z) -{ 2 }-> a__U21(a__U31(mark(X1342), X2342)) :|: X2342 >= 0, z = 1 + (1 + X1342 + X2342), X1342 >= 0 mark(z) -{ 2 }-> a__U21(a__U21(mark(X508))) :|: X508 >= 0, z = 1 + (1 + X508) mark(z) -{ 2 }-> a__U21(a__U12(mark(X506))) :|: X506 >= 0, z = 1 + (1 + X506) mark(z) -{ 2 }-> a__U21(a__U11(mark(X1341), X2341)) :|: z = 1 + (1 + X1341 + X2341), X1341 >= 0, X2341 >= 0 mark(z) -{ 2 }-> a__U21(1) :|: z = 1 + 1 mark(z) -{ 2 }-> a__U21(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__U21(1 + mark(X511)) :|: z = 1 + (1 + X511), X511 >= 0 mark(z) -{ 2 }-> a__U12(a__x(mark(X1340), mark(X2340))) :|: z = 1 + (1 + X1340 + X2340), X2340 >= 0, X1340 >= 0 mark(z) -{ 2 }-> a__U12(a__plus(mark(X1337), mark(X2337))) :|: z = 1 + (1 + X1337 + X2337), X2337 >= 0, X1337 >= 0 mark(z) -{ 2 }-> a__U12(a__isNat(X501)) :|: z = 1 + (1 + X501), X501 >= 0 mark(z) -{ 2 }-> a__U12(a__U72(mark(X1339), X2339, X3171)) :|: X2339 >= 0, X1339 >= 0, z = 1 + (1 + X1339 + X2339 + X3171), X3171 >= 0 mark(z) -{ 2 }-> a__U12(a__U71(mark(X1338), X2338, X3170)) :|: z = 1 + (1 + X1338 + X2338 + X3170), X2338 >= 0, X1338 >= 0, X3170 >= 0 mark(z) -{ 2 }-> a__U12(a__U61(mark(X504))) :|: z = 1 + (1 + X504), X504 >= 0 mark(z) -{ 2 }-> a__U12(a__U52(mark(X1336), X2336, X3169)) :|: X2336 >= 0, z = 1 + (1 + X1336 + X2336 + X3169), X3169 >= 0, X1336 >= 0 mark(z) -{ 2 }-> a__U12(a__U51(mark(X1335), X2335, X3168)) :|: X2335 >= 0, z = 1 + (1 + X1335 + X2335 + X3168), X1335 >= 0, X3168 >= 0 mark(z) -{ 2 }-> a__U12(a__U41(mark(X1334), X2334)) :|: z = 1 + (1 + X1334 + X2334), X1334 >= 0, X2334 >= 0 mark(z) -{ 2 }-> a__U12(a__U32(mark(X503))) :|: z = 1 + (1 + X503), X503 >= 0 mark(z) -{ 2 }-> a__U12(a__U31(mark(X1333), X2333)) :|: X1333 >= 0, z = 1 + (1 + X1333 + X2333), X2333 >= 0 mark(z) -{ 2 }-> a__U12(a__U21(mark(X502))) :|: z = 1 + (1 + X502), X502 >= 0 mark(z) -{ 2 }-> a__U12(a__U12(mark(X500))) :|: z = 1 + (1 + X500), X500 >= 0 mark(z) -{ 2 }-> a__U12(a__U11(mark(X1332), X2332)) :|: z = 1 + (1 + X1332 + X2332), X1332 >= 0, X2332 >= 0 mark(z) -{ 2 }-> a__U12(1) :|: z = 1 + 1 mark(z) -{ 2 }-> a__U12(0) :|: z = 1 + 0 mark(z) -{ 2 }-> a__U12(1 + mark(X505)) :|: z = 1 + (1 + X505), X505 >= 0 mark(z) -{ 2 }-> a__U11(a__x(mark(X1331), mark(X2331)), X2) :|: X2331 >= 0, z = 1 + (1 + X1331 + X2331) + X2, X2 >= 0, X1331 >= 0 mark(z) -{ 2 }-> a__U11(a__plus(mark(X1328), mark(X2328)), X2) :|: z = 1 + (1 + X1328 + X2328) + X2, X2328 >= 0, X1328 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__isNat(X495), X2) :|: z = 1 + (1 + X495) + X2, X2 >= 0, X495 >= 0 mark(z) -{ 2 }-> a__U11(a__U72(mark(X1330), X2330, X3167), X2) :|: X3167 >= 0, X2330 >= 0, X2 >= 0, z = 1 + (1 + X1330 + X2330 + X3167) + X2, X1330 >= 0 mark(z) -{ 2 }-> a__U11(a__U71(mark(X1329), X2329, X3166), X2) :|: X2329 >= 0, X1329 >= 0, X3166 >= 0, z = 1 + (1 + X1329 + X2329 + X3166) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U61(mark(X498)), X2) :|: X498 >= 0, z = 1 + (1 + X498) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U52(mark(X1327), X2327, X3165), X2) :|: X1327 >= 0, X2327 >= 0, X3165 >= 0, z = 1 + (1 + X1327 + X2327 + X3165) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U51(mark(X1326), X2326, X3164), X2) :|: X2326 >= 0, X3164 >= 0, X1326 >= 0, X2 >= 0, z = 1 + (1 + X1326 + X2326 + X3164) + X2 mark(z) -{ 2 }-> a__U11(a__U41(mark(X1325), X2325), X2) :|: X2325 >= 0, z = 1 + (1 + X1325 + X2325) + X2, X1325 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U32(mark(X497)), X2) :|: z = 1 + (1 + X497) + X2, X497 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U31(mark(X1324), X2324), X2) :|: X1324 >= 0, z = 1 + (1 + X1324 + X2324) + X2, X2324 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U21(mark(X496)), X2) :|: z = 1 + (1 + X496) + X2, X496 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U12(mark(X494)), X2) :|: X494 >= 0, z = 1 + (1 + X494) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U11(mark(X1323), X2323), X2) :|: X1323 >= 0, z = 1 + (1 + X1323 + X2323) + X2, X2323 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(1, X2) :|: z = 1 + 1 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(0, X2) :|: z = 1 + 0 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(1 + mark(X499), X2) :|: X499 >= 0, X2 >= 0, z = 1 + (1 + X499) + X2 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0 ---------------------------------------- (33) InliningProof (UPPER BOUND(ID)) Inlined the following terminating rules on right-hand sides where appropriate: a__U12(z) -{ 1 }-> 1 :|: z = 1 a__U12(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U21(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U21(z) -{ 1 }-> 1 :|: z = 1 a__U32(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U32(z) -{ 1 }-> 1 :|: z = 1 a__U61(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U61(z) -{ 1 }-> 0 :|: z = 1 ---------------------------------------- (34) Obligation: Complexity RNTS consisting of the following rules: a__U11(z, z') -{ 2 }-> a__U12(a__U31(a__isNat(V11), V2'')) :|: V11 >= 0, V2'' >= 0, z = 1, z' = 1 + V11 + V2'' a__U11(z, z') -{ 2 }-> a__U12(a__U21(a__isNat(V1''))) :|: V1'' >= 0, z = 1, z' = 1 + V1'' a__U11(z, z') -{ 2 }-> a__U12(a__U11(a__isNat(V1'), V2')) :|: z = 1, z' = 1 + V1' + V2', V2' >= 0, V1' >= 0 a__U11(z, z') -{ 3 }-> 1 :|: z = 1, z' = 0, 1 = 1 a__U11(z, z') -{ 3 }-> 1 :|: z' = V2, z = 1, V2 >= 0, 1 + V2 = 1 a__U11(z, z') -{ 3 }-> 1 + X :|: z = 1, z' = 0, X >= 0, 1 = X a__U11(z, z') -{ 3 }-> 1 + X :|: z' = V2, z = 1, V2 >= 0, X >= 0, 1 + V2 = X a__U11(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U12(z) -{ 1 }-> 1 :|: z = 1 a__U12(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U21(z) -{ 1 }-> 1 :|: z = 1 a__U21(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U31(z, z') -{ 2 }-> a__U32(a__U31(a__isNat(V14), V22)) :|: V14 >= 0, z' = 1 + V14 + V22, z = 1, V22 >= 0 a__U31(z, z') -{ 2 }-> a__U32(a__U21(a__isNat(V13))) :|: V13 >= 0, z = 1, z' = 1 + V13 a__U31(z, z') -{ 2 }-> a__U32(a__U11(a__isNat(V12), V21)) :|: V21 >= 0, z' = 1 + V12 + V21, z = 1, V12 >= 0 a__U31(z, z') -{ 3 }-> 1 :|: z = 1, z' = 0, 1 = 1 a__U31(z, z') -{ 3 }-> 1 :|: z' = V2, z = 1, V2 >= 0, 1 + V2 = 1 a__U31(z, z') -{ 3 }-> 1 + X :|: z = 1, z' = 0, X >= 0, 1 = X a__U31(z, z') -{ 3 }-> 1 + X :|: z' = V2, z = 1, V2 >= 0, X >= 0, 1 + V2 = X a__U31(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U32(z) -{ 1 }-> 1 :|: z = 1 a__U32(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U41(z, z') -{ 1 }-> mark(N) :|: z = 1, z' = N, N >= 0 a__U41(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__U51(z, z', z'') -{ 2 }-> a__U52(a__U31(a__isNat(V17), V24), M, 1 + V17 + V24) :|: z' = M, V24 >= 0, z = 1, z'' = 1 + V17 + V24, M >= 0, V17 >= 0 a__U51(z, z', z'') -{ 2 }-> a__U52(a__U21(a__isNat(V16)), M, 1 + V16) :|: z' = M, z'' = 1 + V16, z = 1, V16 >= 0, M >= 0 a__U51(z, z', z'') -{ 2 }-> a__U52(a__U11(a__isNat(V15), V23), M, 1 + V15 + V23) :|: z' = M, z = 1, V23 >= 0, z'' = 1 + V15 + V23, V15 >= 0, M >= 0 a__U51(z, z', z'') -{ 2 }-> a__U52(1, M, 0) :|: z'' = 0, z' = M, z = 1, M >= 0 a__U51(z, z', z'') -{ 2 }-> a__U52(1 + N, M, N) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0 a__U51(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U52(z, z', z'') -{ 1 }-> 1 + a__plus(mark(N), mark(M)) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0 a__U52(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U61(z) -{ 1 }-> 0 :|: z = 1 a__U61(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__U71(z, z', z'') -{ 2 }-> a__U72(a__U31(a__isNat(V110), V26), M, 1 + V110 + V26) :|: V110 >= 0, z' = M, z = 1, z'' = 1 + V110 + V26, M >= 0, V26 >= 0 a__U71(z, z', z'') -{ 2 }-> a__U72(a__U21(a__isNat(V19)), M, 1 + V19) :|: z' = M, z = 1, V19 >= 0, z'' = 1 + V19, M >= 0 a__U71(z, z', z'') -{ 2 }-> a__U72(a__U11(a__isNat(V18), V25), M, 1 + V18 + V25) :|: z' = M, V25 >= 0, V18 >= 0, z = 1, z'' = 1 + V18 + V25, M >= 0 a__U71(z, z', z'') -{ 2 }-> a__U72(1, M, 0) :|: z'' = 0, z' = M, z = 1, M >= 0 a__U71(z, z', z'') -{ 2 }-> a__U72(1 + N, M, N) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0 a__U71(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__U72(z, z', z'') -{ 1 }-> a__plus(a__x(mark(N), mark(M)), mark(N)) :|: z' = M, z = 1, z'' = N, M >= 0, N >= 0 a__U72(z, z', z'') -{ 1 }-> 1 + X1 + X2 + X3 :|: X1 >= 0, X3 >= 0, X2 >= 0, z = X1, z' = X2, z'' = X3 a__isNat(z) -{ 2 }-> a__U31(a__U31(a__isNat(V119), V212), V2) :|: z = 1 + (1 + V119 + V212) + V2, V2 >= 0, V119 >= 0, V212 >= 0 a__isNat(z) -{ 2 }-> a__U31(a__U21(a__isNat(V118)), V2) :|: V118 >= 0, z = 1 + (1 + V118) + V2, V2 >= 0 a__isNat(z) -{ 2 }-> a__U31(a__U11(a__isNat(V117), V211), V2) :|: z = 1 + (1 + V117 + V211) + V2, V117 >= 0, V2 >= 0, V211 >= 0 a__isNat(z) -{ 2 }-> a__U31(1, V2) :|: V2 >= 0, z = 1 + 0 + V2 a__isNat(z) -{ 2 }-> a__U31(1 + V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNat(z) -{ 2 }-> a__U21(a__U31(a__isNat(V116), V210)) :|: V116 >= 0, V210 >= 0, z = 1 + (1 + V116 + V210) a__isNat(z) -{ 2 }-> a__U21(a__U21(a__isNat(V115))) :|: z = 1 + (1 + V115), V115 >= 0 a__isNat(z) -{ 2 }-> a__U21(a__U11(a__isNat(V114), V29)) :|: V114 >= 0, V29 >= 0, z = 1 + (1 + V114 + V29) a__isNat(z) -{ 2 }-> a__U11(a__U31(a__isNat(V113), V28), V2) :|: V28 >= 0, V2 >= 0, z = 1 + (1 + V113 + V28) + V2, V113 >= 0 a__isNat(z) -{ 2 }-> a__U11(a__U21(a__isNat(V112)), V2) :|: z = 1 + (1 + V112) + V2, V2 >= 0, V112 >= 0 a__isNat(z) -{ 2 }-> a__U11(a__U11(a__isNat(V111), V27), V2) :|: z = 1 + (1 + V111 + V27) + V2, V2 >= 0, V111 >= 0, V27 >= 0 a__isNat(z) -{ 2 }-> a__U11(1, V2) :|: V2 >= 0, z = 1 + 0 + V2 a__isNat(z) -{ 2 }-> a__U11(1 + V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNat(z) -{ 1 }-> 1 :|: z = 0 a__isNat(z) -{ 3 }-> 1 :|: z = 1 + 0, 1 = 1 a__isNat(z) -{ 3 }-> 1 :|: z = 1 + V1, V1 >= 0, 1 + V1 = 1 a__isNat(z) -{ 1 }-> 1 + X :|: X >= 0, z = X a__isNat(z) -{ 3 }-> 1 + X :|: z = 1 + 0, X >= 0, 1 = X a__isNat(z) -{ 3 }-> 1 + X :|: z = 1 + V1, V1 >= 0, X >= 0, 1 + V1 = X a__plus(z, z') -{ 2 }-> a__U51(a__U31(a__isNat(V125), V216), 1 + V125 + V216, N) :|: z' = 1 + (1 + V125 + V216), V125 >= 0, z = N, V216 >= 0, N >= 0 a__plus(z, z') -{ 2 }-> a__U51(a__U21(a__isNat(V124)), 1 + V124, N) :|: V124 >= 0, z = N, z' = 1 + (1 + V124), N >= 0 a__plus(z, z') -{ 2 }-> a__U51(a__U11(a__isNat(V123), V215), 1 + V123 + V215, N) :|: z' = 1 + (1 + V123 + V215), z = N, V215 >= 0, N >= 0, V123 >= 0 a__plus(z, z') -{ 2 }-> a__U51(1, 0, N) :|: z = N, z' = 1 + 0, N >= 0 a__plus(z, z') -{ 2 }-> a__U51(1 + M, M, N) :|: z' = 1 + M, z = N, M >= 0, N >= 0 a__plus(z, z') -{ 2 }-> a__U41(a__U31(a__isNat(V122), V214), 1 + V122 + V214) :|: V122 >= 0, V214 >= 0, z = 1 + V122 + V214, z' = 0 a__plus(z, z') -{ 2 }-> a__U41(a__U21(a__isNat(V121)), 1 + V121) :|: z = 1 + V121, V121 >= 0, z' = 0 a__plus(z, z') -{ 2 }-> a__U41(a__U11(a__isNat(V120), V213), 1 + V120 + V213) :|: V120 >= 0, V213 >= 0, z = 1 + V120 + V213, z' = 0 a__plus(z, z') -{ 2 }-> a__U41(1, 0) :|: z = 0, z' = 0 a__plus(z, z') -{ 2 }-> a__U41(1 + N, N) :|: z = N, z' = 0, N >= 0 a__plus(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 a__x(z, z') -{ 2 }-> a__U71(a__U31(a__isNat(V131), V220), 1 + V131 + V220, N) :|: V131 >= 0, V220 >= 0, z = N, z' = 1 + (1 + V131 + V220), N >= 0 a__x(z, z') -{ 2 }-> a__U71(a__U21(a__isNat(V130)), 1 + V130, N) :|: V130 >= 0, z = N, z' = 1 + (1 + V130), N >= 0 a__x(z, z') -{ 2 }-> a__U71(a__U11(a__isNat(V129), V219), 1 + V129 + V219, N) :|: z = N, z' = 1 + (1 + V129 + V219), V129 >= 0, V219 >= 0, N >= 0 a__x(z, z') -{ 2 }-> a__U71(1, 0, N) :|: z = N, z' = 1 + 0, N >= 0 a__x(z, z') -{ 2 }-> a__U71(1 + M, M, N) :|: z' = 1 + M, z = N, M >= 0, N >= 0 a__x(z, z') -{ 2 }-> a__U61(a__U31(a__isNat(V128), V218)) :|: z = 1 + V128 + V218, V128 >= 0, V218 >= 0, z' = 0 a__x(z, z') -{ 2 }-> a__U61(a__U21(a__isNat(V127))) :|: z = 1 + V127, V127 >= 0, z' = 0 a__x(z, z') -{ 2 }-> a__U61(a__U11(a__isNat(V126), V217)) :|: V217 >= 0, V126 >= 0, z = 1 + V126 + V217, z' = 0 a__x(z, z') -{ 3 }-> 0 :|: z = 0, z' = 0, 1 = 1 a__x(z, z') -{ 3 }-> 0 :|: z = N, z' = 0, N >= 0, 1 + N = 1 a__x(z, z') -{ 3 }-> 1 + X :|: z = 0, z' = 0, X >= 0, 1 = X a__x(z, z') -{ 3 }-> 1 + X :|: z = N, z' = 0, N >= 0, X >= 0, 1 + N = X a__x(z, z') -{ 1 }-> 1 + X1 + X2 :|: X1 >= 0, X2 >= 0, z = X1, z' = X2 mark(z) -{ 1 }-> a__x(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__plus(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__isNat(X) :|: z = 1 + X, X >= 0 mark(z) -{ 2 }-> a__U72(a__x(mark(X1583), mark(X2583)), X2, X3) :|: X1583 >= 0, X2583 >= 0, X3 >= 0, z = 1 + (1 + X1583 + X2583) + X2 + X3, X2 >= 0 mark(z) -{ 2 }-> a__U72(a__plus(mark(X1580), mark(X2580)), X2, X3) :|: X1580 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X1580 + X2580) + X2 + X3, X2580 >= 0 mark(z) -{ 2 }-> a__U72(a__isNat(X663), X2, X3) :|: z = 1 + (1 + X663) + X2 + X3, X3 >= 0, X2 >= 0, X663 >= 0 mark(z) -{ 2 }-> a__U72(a__U72(mark(X1582), X2582, X3279), X2, X3) :|: X2582 >= 0, X3 >= 0, X1582 >= 0, X3279 >= 0, z = 1 + (1 + X1582 + X2582 + X3279) + X2 + X3, X2 >= 0 mark(z) -{ 2 }-> a__U72(a__U71(mark(X1581), X2581, X3278), X2, X3) :|: X1581 >= 0, X3 >= 0, X3278 >= 0, X2 >= 0, z = 1 + (1 + X1581 + X2581 + X3278) + X2 + X3, X2581 >= 0 mark(z) -{ 2 }-> a__U72(a__U61(mark(X666)), X2, X3) :|: z = 1 + (1 + X666) + X2 + X3, X666 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U72(a__U52(mark(X1579), X2579, X3277), X2, X3) :|: X2579 >= 0, X1579 >= 0, X3 >= 0, z = 1 + (1 + X1579 + X2579 + X3277) + X2 + X3, X2 >= 0, X3277 >= 0 mark(z) -{ 2 }-> a__U72(a__U51(mark(X1578), X2578, X3276), X2, X3) :|: z = 1 + (1 + X1578 + X2578 + X3276) + X2 + X3, X1578 >= 0, X3 >= 0, X2 >= 0, X3276 >= 0, X2578 >= 0 mark(z) -{ 2 }-> a__U72(a__U41(mark(X1577), X2577), X2, X3) :|: X1577 >= 0, X3 >= 0, X2577 >= 0, X2 >= 0, z = 1 + (1 + X1577 + X2577) + X2 + X3 mark(z) -{ 2 }-> a__U72(a__U32(mark(X665)), X2, X3) :|: X665 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X665) + X2 + X3 mark(z) -{ 2 }-> a__U72(a__U31(mark(X1576), X2576), X2, X3) :|: z = 1 + (1 + X1576 + X2576) + X2 + X3, X2576 >= 0, X3 >= 0, X2 >= 0, X1576 >= 0 mark(z) -{ 2 }-> a__U72(a__U21(mark(X664)), X2, X3) :|: X664 >= 0, z = 1 + (1 + X664) + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U72(a__U12(mark(X662)), X2, X3) :|: z = 1 + (1 + X662) + X2 + X3, X3 >= 0, X2 >= 0, X662 >= 0 mark(z) -{ 2 }-> a__U72(a__U11(mark(X1575), X2575), X2, X3) :|: X2575 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X1575 + X2575) + X2 + X3, X1575 >= 0 mark(z) -{ 2 }-> a__U72(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U72(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U72(1 + mark(X667), X2, X3) :|: z = 1 + (1 + X667) + X2 + X3, X667 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U71(a__x(mark(X1574), mark(X2574)), X2, X3) :|: X2574 >= 0, X3 >= 0, z = 1 + (1 + X1574 + X2574) + X2 + X3, X2 >= 0, X1574 >= 0 mark(z) -{ 2 }-> a__U71(a__plus(mark(X1571), mark(X2571)), X2, X3) :|: X2571 >= 0, z = 1 + (1 + X1571 + X2571) + X2 + X3, X1571 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U71(a__isNat(X657), X2, X3) :|: z = 1 + (1 + X657) + X2 + X3, X657 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U71(a__U72(mark(X1573), X2573, X3275), X2, X3) :|: X1573 >= 0, X3 >= 0, X2573 >= 0, z = 1 + (1 + X1573 + X2573 + X3275) + X2 + X3, X3275 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U71(a__U71(mark(X1572), X2572, X3274), X2, X3) :|: z = 1 + (1 + X1572 + X2572 + X3274) + X2 + X3, X2572 >= 0, X1572 >= 0, X3 >= 0, X3274 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U71(a__U61(mark(X660)), X2, X3) :|: z = 1 + (1 + X660) + X2 + X3, X660 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U71(a__U52(mark(X1570), X2570, X3273), X2, X3) :|: z = 1 + (1 + X1570 + X2570 + X3273) + X2 + X3, X1570 >= 0, X3273 >= 0, X3 >= 0, X2 >= 0, X2570 >= 0 mark(z) -{ 2 }-> a__U71(a__U51(mark(X1569), X2569, X3272), X2, X3) :|: X2569 >= 0, X3272 >= 0, X1569 >= 0, X3 >= 0, z = 1 + (1 + X1569 + X2569 + X3272) + X2 + X3, X2 >= 0 mark(z) -{ 2 }-> a__U71(a__U41(mark(X1568), X2568), X2, X3) :|: X1568 >= 0, z = 1 + (1 + X1568 + X2568) + X2 + X3, X3 >= 0, X2 >= 0, X2568 >= 0 mark(z) -{ 2 }-> a__U71(a__U32(mark(X659)), X2, X3) :|: z = 1 + (1 + X659) + X2 + X3, X3 >= 0, X659 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U71(a__U31(mark(X1567), X2567), X2, X3) :|: z = 1 + (1 + X1567 + X2567) + X2 + X3, X1567 >= 0, X3 >= 0, X2567 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U71(a__U21(mark(X658)), X2, X3) :|: X658 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X658) + X2 + X3 mark(z) -{ 2 }-> a__U71(a__U12(mark(X656)), X2, X3) :|: z = 1 + (1 + X656) + X2 + X3, X656 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U71(a__U11(mark(X1566), X2566), X2, X3) :|: X3 >= 0, z = 1 + (1 + X1566 + X2566) + X2 + X3, X2566 >= 0, X2 >= 0, X1566 >= 0 mark(z) -{ 2 }-> a__U71(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U71(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U71(1 + mark(X661), X2, X3) :|: z = 1 + (1 + X661) + X2 + X3, X661 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U61(a__x(mark(X1565), mark(X2565))) :|: X2565 >= 0, z = 1 + (1 + X1565 + X2565), X1565 >= 0 mark(z) -{ 2 }-> a__U61(a__plus(mark(X1562), mark(X2562))) :|: z = 1 + (1 + X1562 + X2562), X1562 >= 0, X2562 >= 0 mark(z) -{ 2 }-> a__U61(a__isNat(X651)) :|: X651 >= 0, z = 1 + (1 + X651) mark(z) -{ 2 }-> a__U61(a__U72(mark(X1564), X2564, X3271)) :|: X2564 >= 0, X3271 >= 0, X1564 >= 0, z = 1 + (1 + X1564 + X2564 + X3271) mark(z) -{ 2 }-> a__U61(a__U71(mark(X1563), X2563, X3270)) :|: X1563 >= 0, z = 1 + (1 + X1563 + X2563 + X3270), X2563 >= 0, X3270 >= 0 mark(z) -{ 2 }-> a__U61(a__U61(mark(X654))) :|: X654 >= 0, z = 1 + (1 + X654) mark(z) -{ 2 }-> a__U61(a__U52(mark(X1561), X2561, X3269)) :|: X2561 >= 0, X3269 >= 0, X1561 >= 0, z = 1 + (1 + X1561 + X2561 + X3269) mark(z) -{ 2 }-> a__U61(a__U51(mark(X1560), X2560, X3268)) :|: X1560 >= 0, z = 1 + (1 + X1560 + X2560 + X3268), X3268 >= 0, X2560 >= 0 mark(z) -{ 2 }-> a__U61(a__U41(mark(X1559), X2559)) :|: z = 1 + (1 + X1559 + X2559), X1559 >= 0, X2559 >= 0 mark(z) -{ 2 }-> a__U61(a__U32(mark(X653))) :|: z = 1 + (1 + X653), X653 >= 0 mark(z) -{ 2 }-> a__U61(a__U31(mark(X1558), X2558)) :|: X1558 >= 0, z = 1 + (1 + X1558 + X2558), X2558 >= 0 mark(z) -{ 2 }-> a__U61(a__U21(mark(X652))) :|: X652 >= 0, z = 1 + (1 + X652) mark(z) -{ 2 }-> a__U61(a__U12(mark(X650))) :|: X650 >= 0, z = 1 + (1 + X650) mark(z) -{ 2 }-> a__U61(a__U11(mark(X1557), X2557)) :|: z = 1 + (1 + X1557 + X2557), X1557 >= 0, X2557 >= 0 mark(z) -{ 2 }-> a__U61(1 + mark(X655)) :|: X655 >= 0, z = 1 + (1 + X655) mark(z) -{ 2 }-> a__U52(a__x(mark(X1394), mark(X2394)), X2, X3) :|: X2394 >= 0, z = 1 + (1 + X1394 + X2394) + X2 + X3, X1394 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U52(a__plus(mark(X1391), mark(X2391)), X2, X3) :|: X2391 >= 0, z = 1 + (1 + X1391 + X2391) + X2 + X3, X3 >= 0, X1391 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U52(a__isNat(X537), X2, X3) :|: z = 1 + (1 + X537) + X2 + X3, X537 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U52(a__U72(mark(X1393), X2393, X3195), X2, X3) :|: z = 1 + (1 + X1393 + X2393 + X3195) + X2 + X3, X3195 >= 0, X1393 >= 0, X3 >= 0, X2 >= 0, X2393 >= 0 mark(z) -{ 2 }-> a__U52(a__U71(mark(X1392), X2392, X3194), X2, X3) :|: X1392 >= 0, X3194 >= 0, X3 >= 0, z = 1 + (1 + X1392 + X2392 + X3194) + X2 + X3, X2 >= 0, X2392 >= 0 mark(z) -{ 2 }-> a__U52(a__U61(mark(X540)), X2, X3) :|: z = 1 + (1 + X540) + X2 + X3, X540 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U52(a__U52(mark(X1390), X2390, X3193), X2, X3) :|: X2390 >= 0, z = 1 + (1 + X1390 + X2390 + X3193) + X2 + X3, X3 >= 0, X3193 >= 0, X2 >= 0, X1390 >= 0 mark(z) -{ 2 }-> a__U52(a__U51(mark(X1389), X2389, X3192), X2, X3) :|: X3 >= 0, z = 1 + (1 + X1389 + X2389 + X3192) + X2 + X3, X3192 >= 0, X1389 >= 0, X2389 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U52(a__U41(mark(X1388), X2388), X2, X3) :|: X2388 >= 0, z = 1 + (1 + X1388 + X2388) + X2 + X3, X1388 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U52(a__U32(mark(X539)), X2, X3) :|: z = 1 + (1 + X539) + X2 + X3, X539 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U52(a__U31(mark(X1387), X2387), X2, X3) :|: X2387 >= 0, X3 >= 0, X1387 >= 0, X2 >= 0, z = 1 + (1 + X1387 + X2387) + X2 + X3 mark(z) -{ 2 }-> a__U52(a__U21(mark(X538)), X2, X3) :|: z = 1 + (1 + X538) + X2 + X3, X538 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U52(a__U12(mark(X536)), X2, X3) :|: z = 1 + (1 + X536) + X2 + X3, X3 >= 0, X536 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U52(a__U11(mark(X1386), X2386), X2, X3) :|: X1386 >= 0, X2386 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X1386 + X2386) + X2 + X3 mark(z) -{ 2 }-> a__U52(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U52(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U52(1 + mark(X541), X2, X3) :|: z = 1 + (1 + X541) + X2 + X3, X541 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U51(a__x(mark(X1385), mark(X2385)), X2, X3) :|: X1385 >= 0, X2385 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X1385 + X2385) + X2 + X3 mark(z) -{ 2 }-> a__U51(a__plus(mark(X1382), mark(X2382)), X2, X3) :|: X1382 >= 0, z = 1 + (1 + X1382 + X2382) + X2 + X3, X2382 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U51(a__isNat(X531), X2, X3) :|: z = 1 + (1 + X531) + X2 + X3, X531 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U51(a__U72(mark(X1384), X2384, X3191), X2, X3) :|: X2384 >= 0, X3191 >= 0, z = 1 + (1 + X1384 + X2384 + X3191) + X2 + X3, X1384 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U51(a__U71(mark(X1383), X2383, X3190), X2, X3) :|: z = 1 + (1 + X1383 + X2383 + X3190) + X2 + X3, X1383 >= 0, X3 >= 0, X2383 >= 0, X2 >= 0, X3190 >= 0 mark(z) -{ 2 }-> a__U51(a__U61(mark(X534)), X2, X3) :|: X3 >= 0, X2 >= 0, z = 1 + (1 + X534) + X2 + X3, X534 >= 0 mark(z) -{ 2 }-> a__U51(a__U52(mark(X1381), X2381, X3189), X2, X3) :|: X3 >= 0, X1381 >= 0, X2381 >= 0, X3189 >= 0, X2 >= 0, z = 1 + (1 + X1381 + X2381 + X3189) + X2 + X3 mark(z) -{ 2 }-> a__U51(a__U51(mark(X1380), X2380, X3188), X2, X3) :|: X2380 >= 0, X3188 >= 0, X1380 >= 0, X3 >= 0, z = 1 + (1 + X1380 + X2380 + X3188) + X2 + X3, X2 >= 0 mark(z) -{ 2 }-> a__U51(a__U41(mark(X1379), X2379), X2, X3) :|: z = 1 + (1 + X1379 + X2379) + X2 + X3, X1379 >= 0, X3 >= 0, X2379 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U51(a__U32(mark(X533)), X2, X3) :|: X3 >= 0, z = 1 + (1 + X533) + X2 + X3, X2 >= 0, X533 >= 0 mark(z) -{ 2 }-> a__U51(a__U31(mark(X1378), X2378), X2, X3) :|: X2378 >= 0, z = 1 + (1 + X1378 + X2378) + X2 + X3, X3 >= 0, X2 >= 0, X1378 >= 0 mark(z) -{ 2 }-> a__U51(a__U21(mark(X532)), X2, X3) :|: z = 1 + (1 + X532) + X2 + X3, X3 >= 0, X532 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U51(a__U12(mark(X530)), X2, X3) :|: X530 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X530) + X2 + X3 mark(z) -{ 2 }-> a__U51(a__U11(mark(X1377), X2377), X2, X3) :|: X2377 >= 0, z = 1 + (1 + X1377 + X2377) + X2 + X3, X3 >= 0, X2 >= 0, X1377 >= 0 mark(z) -{ 2 }-> a__U51(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U51(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U51(1 + mark(X535), X2, X3) :|: X3 >= 0, z = 1 + (1 + X535) + X2 + X3, X2 >= 0, X535 >= 0 mark(z) -{ 2 }-> a__U41(a__x(mark(X1376), mark(X2376)), X2) :|: X1376 >= 0, X2376 >= 0, z = 1 + (1 + X1376 + X2376) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__plus(mark(X1373), mark(X2373)), X2) :|: z = 1 + (1 + X1373 + X2373) + X2, X1373 >= 0, X2 >= 0, X2373 >= 0 mark(z) -{ 2 }-> a__U41(a__isNat(X525), X2) :|: z = 1 + (1 + X525) + X2, X2 >= 0, X525 >= 0 mark(z) -{ 2 }-> a__U41(a__U72(mark(X1375), X2375, X3187), X2) :|: X1375 >= 0, z = 1 + (1 + X1375 + X2375 + X3187) + X2, X2375 >= 0, X3187 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U71(mark(X1374), X2374, X3186), X2) :|: X2374 >= 0, X1374 >= 0, z = 1 + (1 + X1374 + X2374 + X3186) + X2, X3186 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U61(mark(X528)), X2) :|: X528 >= 0, z = 1 + (1 + X528) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U52(mark(X1372), X2372, X3185), X2) :|: X1372 >= 0, X3185 >= 0, z = 1 + (1 + X1372 + X2372 + X3185) + X2, X2 >= 0, X2372 >= 0 mark(z) -{ 2 }-> a__U41(a__U51(mark(X1371), X2371, X3184), X2) :|: X1371 >= 0, z = 1 + (1 + X1371 + X2371 + X3184) + X2, X3184 >= 0, X2371 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U41(mark(X1370), X2370), X2) :|: X2370 >= 0, z = 1 + (1 + X1370 + X2370) + X2, X2 >= 0, X1370 >= 0 mark(z) -{ 2 }-> a__U41(a__U32(mark(X527)), X2) :|: X527 >= 0, X2 >= 0, z = 1 + (1 + X527) + X2 mark(z) -{ 2 }-> a__U41(a__U31(mark(X1369), X2369), X2) :|: X1369 >= 0, z = 1 + (1 + X1369 + X2369) + X2, X2369 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U21(mark(X526)), X2) :|: z = 1 + (1 + X526) + X2, X526 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U12(mark(X524)), X2) :|: X2 >= 0, z = 1 + (1 + X524) + X2, X524 >= 0 mark(z) -{ 2 }-> a__U41(a__U11(mark(X1368), X2368), X2) :|: X2368 >= 0, z = 1 + (1 + X1368 + X2368) + X2, X1368 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(1, X2) :|: z = 1 + 1 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U41(0, X2) :|: z = 1 + 0 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U41(1 + mark(X529), X2) :|: z = 1 + (1 + X529) + X2, X529 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U32(a__x(mark(X1367), mark(X2367))) :|: z = 1 + (1 + X1367 + X2367), X2367 >= 0, X1367 >= 0 mark(z) -{ 2 }-> a__U32(a__plus(mark(X1364), mark(X2364))) :|: X1364 >= 0, z = 1 + (1 + X1364 + X2364), X2364 >= 0 mark(z) -{ 2 }-> a__U32(a__isNat(X519)) :|: z = 1 + (1 + X519), X519 >= 0 mark(z) -{ 2 }-> a__U32(a__U72(mark(X1366), X2366, X3183)) :|: X2366 >= 0, X3183 >= 0, z = 1 + (1 + X1366 + X2366 + X3183), X1366 >= 0 mark(z) -{ 2 }-> a__U32(a__U71(mark(X1365), X2365, X3182)) :|: X1365 >= 0, X2365 >= 0, X3182 >= 0, z = 1 + (1 + X1365 + X2365 + X3182) mark(z) -{ 2 }-> a__U32(a__U61(mark(X522))) :|: z = 1 + (1 + X522), X522 >= 0 mark(z) -{ 2 }-> a__U32(a__U52(mark(X1363), X2363, X3181)) :|: X2363 >= 0, X1363 >= 0, X3181 >= 0, z = 1 + (1 + X1363 + X2363 + X3181) mark(z) -{ 2 }-> a__U32(a__U51(mark(X1362), X2362, X3180)) :|: X1362 >= 0, z = 1 + (1 + X1362 + X2362 + X3180), X2362 >= 0, X3180 >= 0 mark(z) -{ 2 }-> a__U32(a__U41(mark(X1361), X2361)) :|: X1361 >= 0, X2361 >= 0, z = 1 + (1 + X1361 + X2361) mark(z) -{ 2 }-> a__U32(a__U32(mark(X521))) :|: X521 >= 0, z = 1 + (1 + X521) mark(z) -{ 2 }-> a__U32(a__U31(mark(X1360), X2360)) :|: X2360 >= 0, X1360 >= 0, z = 1 + (1 + X1360 + X2360) mark(z) -{ 2 }-> a__U32(a__U21(mark(X520))) :|: z = 1 + (1 + X520), X520 >= 0 mark(z) -{ 2 }-> a__U32(a__U12(mark(X518))) :|: X518 >= 0, z = 1 + (1 + X518) mark(z) -{ 2 }-> a__U32(a__U11(mark(X1359), X2359)) :|: z = 1 + (1 + X1359 + X2359), X1359 >= 0, X2359 >= 0 mark(z) -{ 2 }-> a__U32(1 + mark(X523)) :|: z = 1 + (1 + X523), X523 >= 0 mark(z) -{ 2 }-> a__U31(a__x(mark(X1358), mark(X2358)), X2) :|: z = 1 + (1 + X1358 + X2358) + X2, X2358 >= 0, X2 >= 0, X1358 >= 0 mark(z) -{ 2 }-> a__U31(a__plus(mark(X1355), mark(X2355)), X2) :|: X1355 >= 0, z = 1 + (1 + X1355 + X2355) + X2, X2355 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__isNat(X513), X2) :|: X513 >= 0, X2 >= 0, z = 1 + (1 + X513) + X2 mark(z) -{ 2 }-> a__U31(a__U72(mark(X1357), X2357, X3179), X2) :|: z = 1 + (1 + X1357 + X2357 + X3179) + X2, X2357 >= 0, X3179 >= 0, X2 >= 0, X1357 >= 0 mark(z) -{ 2 }-> a__U31(a__U71(mark(X1356), X2356, X3178), X2) :|: X2356 >= 0, X1356 >= 0, X2 >= 0, X3178 >= 0, z = 1 + (1 + X1356 + X2356 + X3178) + X2 mark(z) -{ 2 }-> a__U31(a__U61(mark(X516)), X2) :|: z = 1 + (1 + X516) + X2, X516 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__U52(mark(X1354), X2354, X3177), X2) :|: X1354 >= 0, z = 1 + (1 + X1354 + X2354 + X3177) + X2, X2354 >= 0, X2 >= 0, X3177 >= 0 mark(z) -{ 2 }-> a__U31(a__U51(mark(X1353), X2353, X3176), X2) :|: X1353 >= 0, X3176 >= 0, X2 >= 0, z = 1 + (1 + X1353 + X2353 + X3176) + X2, X2353 >= 0 mark(z) -{ 2 }-> a__U31(a__U41(mark(X1352), X2352), X2) :|: z = 1 + (1 + X1352 + X2352) + X2, X1352 >= 0, X2 >= 0, X2352 >= 0 mark(z) -{ 2 }-> a__U31(a__U32(mark(X515)), X2) :|: z = 1 + (1 + X515) + X2, X515 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__U31(mark(X1351), X2351), X2) :|: X1351 >= 0, z = 1 + (1 + X1351 + X2351) + X2, X2351 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__U21(mark(X514)), X2) :|: z = 1 + (1 + X514) + X2, X2 >= 0, X514 >= 0 mark(z) -{ 2 }-> a__U31(a__U12(mark(X512)), X2) :|: z = 1 + (1 + X512) + X2, X512 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__U11(mark(X1350), X2350), X2) :|: z = 1 + (1 + X1350 + X2350) + X2, X2350 >= 0, X2 >= 0, X1350 >= 0 mark(z) -{ 2 }-> a__U31(1, X2) :|: z = 1 + 1 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U31(0, X2) :|: z = 1 + 0 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U31(1 + mark(X517), X2) :|: X517 >= 0, z = 1 + (1 + X517) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__x(mark(X1349), mark(X2349))) :|: z = 1 + (1 + X1349 + X2349), X1349 >= 0, X2349 >= 0 mark(z) -{ 2 }-> a__U21(a__plus(mark(X1346), mark(X2346))) :|: X2346 >= 0, X1346 >= 0, z = 1 + (1 + X1346 + X2346) mark(z) -{ 2 }-> a__U21(a__isNat(X507)) :|: X507 >= 0, z = 1 + (1 + X507) mark(z) -{ 2 }-> a__U21(a__U72(mark(X1348), X2348, X3175)) :|: X1348 >= 0, X3175 >= 0, X2348 >= 0, z = 1 + (1 + X1348 + X2348 + X3175) mark(z) -{ 2 }-> a__U21(a__U71(mark(X1347), X2347, X3174)) :|: z = 1 + (1 + X1347 + X2347 + X3174), X2347 >= 0, X3174 >= 0, X1347 >= 0 mark(z) -{ 2 }-> a__U21(a__U61(mark(X510))) :|: z = 1 + (1 + X510), X510 >= 0 mark(z) -{ 2 }-> a__U21(a__U52(mark(X1345), X2345, X3173)) :|: z = 1 + (1 + X1345 + X2345 + X3173), X1345 >= 0, X2345 >= 0, X3173 >= 0 mark(z) -{ 2 }-> a__U21(a__U51(mark(X1344), X2344, X3172)) :|: X1344 >= 0, z = 1 + (1 + X1344 + X2344 + X3172), X2344 >= 0, X3172 >= 0 mark(z) -{ 2 }-> a__U21(a__U41(mark(X1343), X2343)) :|: z = 1 + (1 + X1343 + X2343), X1343 >= 0, X2343 >= 0 mark(z) -{ 2 }-> a__U21(a__U32(mark(X509))) :|: X509 >= 0, z = 1 + (1 + X509) mark(z) -{ 2 }-> a__U21(a__U31(mark(X1342), X2342)) :|: X2342 >= 0, z = 1 + (1 + X1342 + X2342), X1342 >= 0 mark(z) -{ 2 }-> a__U21(a__U21(mark(X508))) :|: X508 >= 0, z = 1 + (1 + X508) mark(z) -{ 2 }-> a__U21(a__U12(mark(X506))) :|: X506 >= 0, z = 1 + (1 + X506) mark(z) -{ 2 }-> a__U21(a__U11(mark(X1341), X2341)) :|: z = 1 + (1 + X1341 + X2341), X1341 >= 0, X2341 >= 0 mark(z) -{ 2 }-> a__U21(1 + mark(X511)) :|: z = 1 + (1 + X511), X511 >= 0 mark(z) -{ 2 }-> a__U12(a__x(mark(X1340), mark(X2340))) :|: z = 1 + (1 + X1340 + X2340), X2340 >= 0, X1340 >= 0 mark(z) -{ 2 }-> a__U12(a__plus(mark(X1337), mark(X2337))) :|: z = 1 + (1 + X1337 + X2337), X2337 >= 0, X1337 >= 0 mark(z) -{ 2 }-> a__U12(a__isNat(X501)) :|: z = 1 + (1 + X501), X501 >= 0 mark(z) -{ 2 }-> a__U12(a__U72(mark(X1339), X2339, X3171)) :|: X2339 >= 0, X1339 >= 0, z = 1 + (1 + X1339 + X2339 + X3171), X3171 >= 0 mark(z) -{ 2 }-> a__U12(a__U71(mark(X1338), X2338, X3170)) :|: z = 1 + (1 + X1338 + X2338 + X3170), X2338 >= 0, X1338 >= 0, X3170 >= 0 mark(z) -{ 2 }-> a__U12(a__U61(mark(X504))) :|: z = 1 + (1 + X504), X504 >= 0 mark(z) -{ 2 }-> a__U12(a__U52(mark(X1336), X2336, X3169)) :|: X2336 >= 0, z = 1 + (1 + X1336 + X2336 + X3169), X3169 >= 0, X1336 >= 0 mark(z) -{ 2 }-> a__U12(a__U51(mark(X1335), X2335, X3168)) :|: X2335 >= 0, z = 1 + (1 + X1335 + X2335 + X3168), X1335 >= 0, X3168 >= 0 mark(z) -{ 2 }-> a__U12(a__U41(mark(X1334), X2334)) :|: z = 1 + (1 + X1334 + X2334), X1334 >= 0, X2334 >= 0 mark(z) -{ 2 }-> a__U12(a__U32(mark(X503))) :|: z = 1 + (1 + X503), X503 >= 0 mark(z) -{ 2 }-> a__U12(a__U31(mark(X1333), X2333)) :|: X1333 >= 0, z = 1 + (1 + X1333 + X2333), X2333 >= 0 mark(z) -{ 2 }-> a__U12(a__U21(mark(X502))) :|: z = 1 + (1 + X502), X502 >= 0 mark(z) -{ 2 }-> a__U12(a__U12(mark(X500))) :|: z = 1 + (1 + X500), X500 >= 0 mark(z) -{ 2 }-> a__U12(a__U11(mark(X1332), X2332)) :|: z = 1 + (1 + X1332 + X2332), X1332 >= 0, X2332 >= 0 mark(z) -{ 2 }-> a__U12(1 + mark(X505)) :|: z = 1 + (1 + X505), X505 >= 0 mark(z) -{ 2 }-> a__U11(a__x(mark(X1331), mark(X2331)), X2) :|: X2331 >= 0, z = 1 + (1 + X1331 + X2331) + X2, X2 >= 0, X1331 >= 0 mark(z) -{ 2 }-> a__U11(a__plus(mark(X1328), mark(X2328)), X2) :|: z = 1 + (1 + X1328 + X2328) + X2, X2328 >= 0, X1328 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__isNat(X495), X2) :|: z = 1 + (1 + X495) + X2, X2 >= 0, X495 >= 0 mark(z) -{ 2 }-> a__U11(a__U72(mark(X1330), X2330, X3167), X2) :|: X3167 >= 0, X2330 >= 0, X2 >= 0, z = 1 + (1 + X1330 + X2330 + X3167) + X2, X1330 >= 0 mark(z) -{ 2 }-> a__U11(a__U71(mark(X1329), X2329, X3166), X2) :|: X2329 >= 0, X1329 >= 0, X3166 >= 0, z = 1 + (1 + X1329 + X2329 + X3166) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U61(mark(X498)), X2) :|: X498 >= 0, z = 1 + (1 + X498) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U52(mark(X1327), X2327, X3165), X2) :|: X1327 >= 0, X2327 >= 0, X3165 >= 0, z = 1 + (1 + X1327 + X2327 + X3165) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U51(mark(X1326), X2326, X3164), X2) :|: X2326 >= 0, X3164 >= 0, X1326 >= 0, X2 >= 0, z = 1 + (1 + X1326 + X2326 + X3164) + X2 mark(z) -{ 2 }-> a__U11(a__U41(mark(X1325), X2325), X2) :|: X2325 >= 0, z = 1 + (1 + X1325 + X2325) + X2, X1325 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U32(mark(X497)), X2) :|: z = 1 + (1 + X497) + X2, X497 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U31(mark(X1324), X2324), X2) :|: X1324 >= 0, z = 1 + (1 + X1324 + X2324) + X2, X2324 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U21(mark(X496)), X2) :|: z = 1 + (1 + X496) + X2, X496 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U12(mark(X494)), X2) :|: X494 >= 0, z = 1 + (1 + X494) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U11(mark(X1323), X2323), X2) :|: X1323 >= 0, z = 1 + (1 + X1323 + X2323) + X2, X2323 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(1, X2) :|: z = 1 + 1 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(0, X2) :|: z = 1 + 0 + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(1 + mark(X499), X2) :|: X499 >= 0, X2 >= 0, z = 1 + (1 + X499) + X2 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 3 }-> 1 :|: z = 1 + 1, 1 = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 3 }-> 0 :|: z = 1 + 1, 1 = 1 mark(z) -{ 3 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X mark(z) -{ 3 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X mark(z) -{ 1 }-> 1 + mark(X) :|: z = 1 + X, X >= 0 ---------------------------------------- (35) SimplificationProof (BOTH BOUNDS(ID, ID)) Simplified the RNTS by moving equalities from the constraints into the right-hand sides. ---------------------------------------- (36) Obligation: Complexity RNTS consisting of the following rules: a__U11(z, z') -{ 2 }-> a__U12(a__U31(a__isNat(V11), V2'')) :|: V11 >= 0, V2'' >= 0, z = 1, z' = 1 + V11 + V2'' a__U11(z, z') -{ 2 }-> a__U12(a__U21(a__isNat(z' - 1))) :|: z' - 1 >= 0, z = 1 a__U11(z, z') -{ 2 }-> a__U12(a__U11(a__isNat(V1'), V2')) :|: z = 1, z' = 1 + V1' + V2', V2' >= 0, V1' >= 0 a__U11(z, z') -{ 3 }-> 1 :|: z = 1, z' = 0, 1 = 1 a__U11(z, z') -{ 3 }-> 1 :|: z = 1, z' >= 0, 1 + z' = 1 a__U11(z, z') -{ 3 }-> 1 + X :|: z = 1, z' = 0, X >= 0, 1 = X a__U11(z, z') -{ 3 }-> 1 + X :|: z = 1, z' >= 0, X >= 0, 1 + z' = X a__U11(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__U12(z) -{ 1 }-> 1 :|: z = 1 a__U12(z) -{ 1 }-> 1 + z :|: z >= 0 a__U21(z) -{ 1 }-> 1 :|: z = 1 a__U21(z) -{ 1 }-> 1 + z :|: z >= 0 a__U31(z, z') -{ 2 }-> a__U32(a__U31(a__isNat(V14), V22)) :|: V14 >= 0, z' = 1 + V14 + V22, z = 1, V22 >= 0 a__U31(z, z') -{ 2 }-> a__U32(a__U21(a__isNat(z' - 1))) :|: z' - 1 >= 0, z = 1 a__U31(z, z') -{ 2 }-> a__U32(a__U11(a__isNat(V12), V21)) :|: V21 >= 0, z' = 1 + V12 + V21, z = 1, V12 >= 0 a__U31(z, z') -{ 3 }-> 1 :|: z = 1, z' = 0, 1 = 1 a__U31(z, z') -{ 3 }-> 1 :|: z = 1, z' >= 0, 1 + z' = 1 a__U31(z, z') -{ 3 }-> 1 + X :|: z = 1, z' = 0, X >= 0, 1 = X a__U31(z, z') -{ 3 }-> 1 + X :|: z = 1, z' >= 0, X >= 0, 1 + z' = X a__U31(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__U32(z) -{ 1 }-> 1 :|: z = 1 a__U32(z) -{ 1 }-> 1 + z :|: z >= 0 a__U41(z, z') -{ 1 }-> mark(z') :|: z = 1, z' >= 0 a__U41(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__U51(z, z', z'') -{ 2 }-> a__U52(a__U31(a__isNat(V17), V24), z', 1 + V17 + V24) :|: V24 >= 0, z = 1, z'' = 1 + V17 + V24, z' >= 0, V17 >= 0 a__U51(z, z', z'') -{ 2 }-> a__U52(a__U21(a__isNat(z'' - 1)), z', 1 + (z'' - 1)) :|: z = 1, z'' - 1 >= 0, z' >= 0 a__U51(z, z', z'') -{ 2 }-> a__U52(a__U11(a__isNat(V15), V23), z', 1 + V15 + V23) :|: z = 1, V23 >= 0, z'' = 1 + V15 + V23, V15 >= 0, z' >= 0 a__U51(z, z', z'') -{ 2 }-> a__U52(1, z', 0) :|: z'' = 0, z = 1, z' >= 0 a__U51(z, z', z'') -{ 2 }-> a__U52(1 + z'', z', z'') :|: z = 1, z' >= 0, z'' >= 0 a__U51(z, z', z'') -{ 1 }-> 1 + z + z' + z'' :|: z >= 0, z'' >= 0, z' >= 0 a__U52(z, z', z'') -{ 1 }-> 1 + a__plus(mark(z''), mark(z')) :|: z = 1, z' >= 0, z'' >= 0 a__U52(z, z', z'') -{ 1 }-> 1 + z + z' + z'' :|: z >= 0, z'' >= 0, z' >= 0 a__U61(z) -{ 1 }-> 0 :|: z = 1 a__U61(z) -{ 1 }-> 1 + z :|: z >= 0 a__U71(z, z', z'') -{ 2 }-> a__U72(a__U31(a__isNat(V110), V26), z', 1 + V110 + V26) :|: V110 >= 0, z = 1, z'' = 1 + V110 + V26, z' >= 0, V26 >= 0 a__U71(z, z', z'') -{ 2 }-> a__U72(a__U21(a__isNat(z'' - 1)), z', 1 + (z'' - 1)) :|: z = 1, z'' - 1 >= 0, z' >= 0 a__U71(z, z', z'') -{ 2 }-> a__U72(a__U11(a__isNat(V18), V25), z', 1 + V18 + V25) :|: V25 >= 0, V18 >= 0, z = 1, z'' = 1 + V18 + V25, z' >= 0 a__U71(z, z', z'') -{ 2 }-> a__U72(1, z', 0) :|: z'' = 0, z = 1, z' >= 0 a__U71(z, z', z'') -{ 2 }-> a__U72(1 + z'', z', z'') :|: z = 1, z' >= 0, z'' >= 0 a__U71(z, z', z'') -{ 1 }-> 1 + z + z' + z'' :|: z >= 0, z'' >= 0, z' >= 0 a__U72(z, z', z'') -{ 1 }-> a__plus(a__x(mark(z''), mark(z')), mark(z'')) :|: z = 1, z' >= 0, z'' >= 0 a__U72(z, z', z'') -{ 1 }-> 1 + z + z' + z'' :|: z >= 0, z'' >= 0, z' >= 0 a__isNat(z) -{ 2 }-> a__U31(a__U31(a__isNat(V119), V212), V2) :|: z = 1 + (1 + V119 + V212) + V2, V2 >= 0, V119 >= 0, V212 >= 0 a__isNat(z) -{ 2 }-> a__U31(a__U21(a__isNat(V118)), V2) :|: V118 >= 0, z = 1 + (1 + V118) + V2, V2 >= 0 a__isNat(z) -{ 2 }-> a__U31(a__U11(a__isNat(V117), V211), V2) :|: z = 1 + (1 + V117 + V211) + V2, V117 >= 0, V2 >= 0, V211 >= 0 a__isNat(z) -{ 2 }-> a__U31(1, z - 1) :|: z - 1 >= 0 a__isNat(z) -{ 2 }-> a__U31(1 + V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNat(z) -{ 2 }-> a__U21(a__U31(a__isNat(V116), V210)) :|: V116 >= 0, V210 >= 0, z = 1 + (1 + V116 + V210) a__isNat(z) -{ 2 }-> a__U21(a__U21(a__isNat(z - 2))) :|: z - 2 >= 0 a__isNat(z) -{ 2 }-> a__U21(a__U11(a__isNat(V114), V29)) :|: V114 >= 0, V29 >= 0, z = 1 + (1 + V114 + V29) a__isNat(z) -{ 2 }-> a__U11(a__U31(a__isNat(V113), V28), V2) :|: V28 >= 0, V2 >= 0, z = 1 + (1 + V113 + V28) + V2, V113 >= 0 a__isNat(z) -{ 2 }-> a__U11(a__U21(a__isNat(V112)), V2) :|: z = 1 + (1 + V112) + V2, V2 >= 0, V112 >= 0 a__isNat(z) -{ 2 }-> a__U11(a__U11(a__isNat(V111), V27), V2) :|: z = 1 + (1 + V111 + V27) + V2, V2 >= 0, V111 >= 0, V27 >= 0 a__isNat(z) -{ 2 }-> a__U11(1, z - 1) :|: z - 1 >= 0 a__isNat(z) -{ 2 }-> a__U11(1 + V1, V2) :|: V1 >= 0, V2 >= 0, z = 1 + V1 + V2 a__isNat(z) -{ 1 }-> 1 :|: z = 0 a__isNat(z) -{ 3 }-> 1 :|: z = 1 + 0, 1 = 1 a__isNat(z) -{ 3 }-> 1 :|: z - 1 >= 0, 1 + (z - 1) = 1 a__isNat(z) -{ 3 }-> 1 + X :|: z = 1 + 0, X >= 0, 1 = X a__isNat(z) -{ 3 }-> 1 + X :|: z - 1 >= 0, X >= 0, 1 + (z - 1) = X a__isNat(z) -{ 1 }-> 1 + z :|: z >= 0 a__plus(z, z') -{ 2 }-> a__U51(a__U31(a__isNat(V125), V216), 1 + V125 + V216, z) :|: z' = 1 + (1 + V125 + V216), V125 >= 0, V216 >= 0, z >= 0 a__plus(z, z') -{ 2 }-> a__U51(a__U21(a__isNat(z' - 2)), 1 + (z' - 2), z) :|: z' - 2 >= 0, z >= 0 a__plus(z, z') -{ 2 }-> a__U51(a__U11(a__isNat(V123), V215), 1 + V123 + V215, z) :|: z' = 1 + (1 + V123 + V215), V215 >= 0, z >= 0, V123 >= 0 a__plus(z, z') -{ 2 }-> a__U51(1, 0, z) :|: z' = 1 + 0, z >= 0 a__plus(z, z') -{ 2 }-> a__U51(1 + (z' - 1), z' - 1, z) :|: z' - 1 >= 0, z >= 0 a__plus(z, z') -{ 2 }-> a__U41(a__U31(a__isNat(V122), V214), 1 + V122 + V214) :|: V122 >= 0, V214 >= 0, z = 1 + V122 + V214, z' = 0 a__plus(z, z') -{ 2 }-> a__U41(a__U21(a__isNat(z - 1)), 1 + (z - 1)) :|: z - 1 >= 0, z' = 0 a__plus(z, z') -{ 2 }-> a__U41(a__U11(a__isNat(V120), V213), 1 + V120 + V213) :|: V120 >= 0, V213 >= 0, z = 1 + V120 + V213, z' = 0 a__plus(z, z') -{ 2 }-> a__U41(1, 0) :|: z = 0, z' = 0 a__plus(z, z') -{ 2 }-> a__U41(1 + z, z) :|: z' = 0, z >= 0 a__plus(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 a__x(z, z') -{ 2 }-> a__U71(a__U31(a__isNat(V131), V220), 1 + V131 + V220, z) :|: V131 >= 0, V220 >= 0, z' = 1 + (1 + V131 + V220), z >= 0 a__x(z, z') -{ 2 }-> a__U71(a__U21(a__isNat(z' - 2)), 1 + (z' - 2), z) :|: z' - 2 >= 0, z >= 0 a__x(z, z') -{ 2 }-> a__U71(a__U11(a__isNat(V129), V219), 1 + V129 + V219, z) :|: z' = 1 + (1 + V129 + V219), V129 >= 0, V219 >= 0, z >= 0 a__x(z, z') -{ 2 }-> a__U71(1, 0, z) :|: z' = 1 + 0, z >= 0 a__x(z, z') -{ 2 }-> a__U71(1 + (z' - 1), z' - 1, z) :|: z' - 1 >= 0, z >= 0 a__x(z, z') -{ 2 }-> a__U61(a__U31(a__isNat(V128), V218)) :|: z = 1 + V128 + V218, V128 >= 0, V218 >= 0, z' = 0 a__x(z, z') -{ 2 }-> a__U61(a__U21(a__isNat(z - 1))) :|: z - 1 >= 0, z' = 0 a__x(z, z') -{ 2 }-> a__U61(a__U11(a__isNat(V126), V217)) :|: V217 >= 0, V126 >= 0, z = 1 + V126 + V217, z' = 0 a__x(z, z') -{ 3 }-> 0 :|: z = 0, z' = 0, 1 = 1 a__x(z, z') -{ 3 }-> 0 :|: z' = 0, z >= 0, 1 + z = 1 a__x(z, z') -{ 3 }-> 1 + X :|: z = 0, z' = 0, X >= 0, 1 = X a__x(z, z') -{ 3 }-> 1 + X :|: z' = 0, z >= 0, X >= 0, 1 + z = X a__x(z, z') -{ 1 }-> 1 + z + z' :|: z >= 0, z' >= 0 mark(z) -{ 1 }-> a__x(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__plus(mark(X1), mark(X2)) :|: X1 >= 0, X2 >= 0, z = 1 + X1 + X2 mark(z) -{ 1 }-> a__isNat(z - 1) :|: z - 1 >= 0 mark(z) -{ 2 }-> a__U72(a__x(mark(X1583), mark(X2583)), X2, X3) :|: X1583 >= 0, X2583 >= 0, X3 >= 0, z = 1 + (1 + X1583 + X2583) + X2 + X3, X2 >= 0 mark(z) -{ 2 }-> a__U72(a__plus(mark(X1580), mark(X2580)), X2, X3) :|: X1580 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X1580 + X2580) + X2 + X3, X2580 >= 0 mark(z) -{ 2 }-> a__U72(a__isNat(X663), X2, X3) :|: z = 1 + (1 + X663) + X2 + X3, X3 >= 0, X2 >= 0, X663 >= 0 mark(z) -{ 2 }-> a__U72(a__U72(mark(X1582), X2582, X3279), X2, X3) :|: X2582 >= 0, X3 >= 0, X1582 >= 0, X3279 >= 0, z = 1 + (1 + X1582 + X2582 + X3279) + X2 + X3, X2 >= 0 mark(z) -{ 2 }-> a__U72(a__U71(mark(X1581), X2581, X3278), X2, X3) :|: X1581 >= 0, X3 >= 0, X3278 >= 0, X2 >= 0, z = 1 + (1 + X1581 + X2581 + X3278) + X2 + X3, X2581 >= 0 mark(z) -{ 2 }-> a__U72(a__U61(mark(X666)), X2, X3) :|: z = 1 + (1 + X666) + X2 + X3, X666 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U72(a__U52(mark(X1579), X2579, X3277), X2, X3) :|: X2579 >= 0, X1579 >= 0, X3 >= 0, z = 1 + (1 + X1579 + X2579 + X3277) + X2 + X3, X2 >= 0, X3277 >= 0 mark(z) -{ 2 }-> a__U72(a__U51(mark(X1578), X2578, X3276), X2, X3) :|: z = 1 + (1 + X1578 + X2578 + X3276) + X2 + X3, X1578 >= 0, X3 >= 0, X2 >= 0, X3276 >= 0, X2578 >= 0 mark(z) -{ 2 }-> a__U72(a__U41(mark(X1577), X2577), X2, X3) :|: X1577 >= 0, X3 >= 0, X2577 >= 0, X2 >= 0, z = 1 + (1 + X1577 + X2577) + X2 + X3 mark(z) -{ 2 }-> a__U72(a__U32(mark(X665)), X2, X3) :|: X665 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X665) + X2 + X3 mark(z) -{ 2 }-> a__U72(a__U31(mark(X1576), X2576), X2, X3) :|: z = 1 + (1 + X1576 + X2576) + X2 + X3, X2576 >= 0, X3 >= 0, X2 >= 0, X1576 >= 0 mark(z) -{ 2 }-> a__U72(a__U21(mark(X664)), X2, X3) :|: X664 >= 0, z = 1 + (1 + X664) + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U72(a__U12(mark(X662)), X2, X3) :|: z = 1 + (1 + X662) + X2 + X3, X3 >= 0, X2 >= 0, X662 >= 0 mark(z) -{ 2 }-> a__U72(a__U11(mark(X1575), X2575), X2, X3) :|: X2575 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X1575 + X2575) + X2 + X3, X1575 >= 0 mark(z) -{ 2 }-> a__U72(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U72(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U72(1 + mark(X667), X2, X3) :|: z = 1 + (1 + X667) + X2 + X3, X667 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U71(a__x(mark(X1574), mark(X2574)), X2, X3) :|: X2574 >= 0, X3 >= 0, z = 1 + (1 + X1574 + X2574) + X2 + X3, X2 >= 0, X1574 >= 0 mark(z) -{ 2 }-> a__U71(a__plus(mark(X1571), mark(X2571)), X2, X3) :|: X2571 >= 0, z = 1 + (1 + X1571 + X2571) + X2 + X3, X1571 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U71(a__isNat(X657), X2, X3) :|: z = 1 + (1 + X657) + X2 + X3, X657 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U71(a__U72(mark(X1573), X2573, X3275), X2, X3) :|: X1573 >= 0, X3 >= 0, X2573 >= 0, z = 1 + (1 + X1573 + X2573 + X3275) + X2 + X3, X3275 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U71(a__U71(mark(X1572), X2572, X3274), X2, X3) :|: z = 1 + (1 + X1572 + X2572 + X3274) + X2 + X3, X2572 >= 0, X1572 >= 0, X3 >= 0, X3274 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U71(a__U61(mark(X660)), X2, X3) :|: z = 1 + (1 + X660) + X2 + X3, X660 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U71(a__U52(mark(X1570), X2570, X3273), X2, X3) :|: z = 1 + (1 + X1570 + X2570 + X3273) + X2 + X3, X1570 >= 0, X3273 >= 0, X3 >= 0, X2 >= 0, X2570 >= 0 mark(z) -{ 2 }-> a__U71(a__U51(mark(X1569), X2569, X3272), X2, X3) :|: X2569 >= 0, X3272 >= 0, X1569 >= 0, X3 >= 0, z = 1 + (1 + X1569 + X2569 + X3272) + X2 + X3, X2 >= 0 mark(z) -{ 2 }-> a__U71(a__U41(mark(X1568), X2568), X2, X3) :|: X1568 >= 0, z = 1 + (1 + X1568 + X2568) + X2 + X3, X3 >= 0, X2 >= 0, X2568 >= 0 mark(z) -{ 2 }-> a__U71(a__U32(mark(X659)), X2, X3) :|: z = 1 + (1 + X659) + X2 + X3, X3 >= 0, X659 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U71(a__U31(mark(X1567), X2567), X2, X3) :|: z = 1 + (1 + X1567 + X2567) + X2 + X3, X1567 >= 0, X3 >= 0, X2567 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U71(a__U21(mark(X658)), X2, X3) :|: X658 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X658) + X2 + X3 mark(z) -{ 2 }-> a__U71(a__U12(mark(X656)), X2, X3) :|: z = 1 + (1 + X656) + X2 + X3, X656 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U71(a__U11(mark(X1566), X2566), X2, X3) :|: X3 >= 0, z = 1 + (1 + X1566 + X2566) + X2 + X3, X2566 >= 0, X2 >= 0, X1566 >= 0 mark(z) -{ 2 }-> a__U71(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U71(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U71(1 + mark(X661), X2, X3) :|: z = 1 + (1 + X661) + X2 + X3, X661 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U61(a__x(mark(X1565), mark(X2565))) :|: X2565 >= 0, z = 1 + (1 + X1565 + X2565), X1565 >= 0 mark(z) -{ 2 }-> a__U61(a__plus(mark(X1562), mark(X2562))) :|: z = 1 + (1 + X1562 + X2562), X1562 >= 0, X2562 >= 0 mark(z) -{ 2 }-> a__U61(a__isNat(z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U61(a__U72(mark(X1564), X2564, X3271)) :|: X2564 >= 0, X3271 >= 0, X1564 >= 0, z = 1 + (1 + X1564 + X2564 + X3271) mark(z) -{ 2 }-> a__U61(a__U71(mark(X1563), X2563, X3270)) :|: X1563 >= 0, z = 1 + (1 + X1563 + X2563 + X3270), X2563 >= 0, X3270 >= 0 mark(z) -{ 2 }-> a__U61(a__U61(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U61(a__U52(mark(X1561), X2561, X3269)) :|: X2561 >= 0, X3269 >= 0, X1561 >= 0, z = 1 + (1 + X1561 + X2561 + X3269) mark(z) -{ 2 }-> a__U61(a__U51(mark(X1560), X2560, X3268)) :|: X1560 >= 0, z = 1 + (1 + X1560 + X2560 + X3268), X3268 >= 0, X2560 >= 0 mark(z) -{ 2 }-> a__U61(a__U41(mark(X1559), X2559)) :|: z = 1 + (1 + X1559 + X2559), X1559 >= 0, X2559 >= 0 mark(z) -{ 2 }-> a__U61(a__U32(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U61(a__U31(mark(X1558), X2558)) :|: X1558 >= 0, z = 1 + (1 + X1558 + X2558), X2558 >= 0 mark(z) -{ 2 }-> a__U61(a__U21(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U61(a__U12(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U61(a__U11(mark(X1557), X2557)) :|: z = 1 + (1 + X1557 + X2557), X1557 >= 0, X2557 >= 0 mark(z) -{ 2 }-> a__U61(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U52(a__x(mark(X1394), mark(X2394)), X2, X3) :|: X2394 >= 0, z = 1 + (1 + X1394 + X2394) + X2 + X3, X1394 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U52(a__plus(mark(X1391), mark(X2391)), X2, X3) :|: X2391 >= 0, z = 1 + (1 + X1391 + X2391) + X2 + X3, X3 >= 0, X1391 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U52(a__isNat(X537), X2, X3) :|: z = 1 + (1 + X537) + X2 + X3, X537 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U52(a__U72(mark(X1393), X2393, X3195), X2, X3) :|: z = 1 + (1 + X1393 + X2393 + X3195) + X2 + X3, X3195 >= 0, X1393 >= 0, X3 >= 0, X2 >= 0, X2393 >= 0 mark(z) -{ 2 }-> a__U52(a__U71(mark(X1392), X2392, X3194), X2, X3) :|: X1392 >= 0, X3194 >= 0, X3 >= 0, z = 1 + (1 + X1392 + X2392 + X3194) + X2 + X3, X2 >= 0, X2392 >= 0 mark(z) -{ 2 }-> a__U52(a__U61(mark(X540)), X2, X3) :|: z = 1 + (1 + X540) + X2 + X3, X540 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U52(a__U52(mark(X1390), X2390, X3193), X2, X3) :|: X2390 >= 0, z = 1 + (1 + X1390 + X2390 + X3193) + X2 + X3, X3 >= 0, X3193 >= 0, X2 >= 0, X1390 >= 0 mark(z) -{ 2 }-> a__U52(a__U51(mark(X1389), X2389, X3192), X2, X3) :|: X3 >= 0, z = 1 + (1 + X1389 + X2389 + X3192) + X2 + X3, X3192 >= 0, X1389 >= 0, X2389 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U52(a__U41(mark(X1388), X2388), X2, X3) :|: X2388 >= 0, z = 1 + (1 + X1388 + X2388) + X2 + X3, X1388 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U52(a__U32(mark(X539)), X2, X3) :|: z = 1 + (1 + X539) + X2 + X3, X539 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U52(a__U31(mark(X1387), X2387), X2, X3) :|: X2387 >= 0, X3 >= 0, X1387 >= 0, X2 >= 0, z = 1 + (1 + X1387 + X2387) + X2 + X3 mark(z) -{ 2 }-> a__U52(a__U21(mark(X538)), X2, X3) :|: z = 1 + (1 + X538) + X2 + X3, X538 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U52(a__U12(mark(X536)), X2, X3) :|: z = 1 + (1 + X536) + X2 + X3, X3 >= 0, X536 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U52(a__U11(mark(X1386), X2386), X2, X3) :|: X1386 >= 0, X2386 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X1386 + X2386) + X2 + X3 mark(z) -{ 2 }-> a__U52(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U52(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U52(1 + mark(X541), X2, X3) :|: z = 1 + (1 + X541) + X2 + X3, X541 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U51(a__x(mark(X1385), mark(X2385)), X2, X3) :|: X1385 >= 0, X2385 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X1385 + X2385) + X2 + X3 mark(z) -{ 2 }-> a__U51(a__plus(mark(X1382), mark(X2382)), X2, X3) :|: X1382 >= 0, z = 1 + (1 + X1382 + X2382) + X2 + X3, X2382 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U51(a__isNat(X531), X2, X3) :|: z = 1 + (1 + X531) + X2 + X3, X531 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U51(a__U72(mark(X1384), X2384, X3191), X2, X3) :|: X2384 >= 0, X3191 >= 0, z = 1 + (1 + X1384 + X2384 + X3191) + X2 + X3, X1384 >= 0, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U51(a__U71(mark(X1383), X2383, X3190), X2, X3) :|: z = 1 + (1 + X1383 + X2383 + X3190) + X2 + X3, X1383 >= 0, X3 >= 0, X2383 >= 0, X2 >= 0, X3190 >= 0 mark(z) -{ 2 }-> a__U51(a__U61(mark(X534)), X2, X3) :|: X3 >= 0, X2 >= 0, z = 1 + (1 + X534) + X2 + X3, X534 >= 0 mark(z) -{ 2 }-> a__U51(a__U52(mark(X1381), X2381, X3189), X2, X3) :|: X3 >= 0, X1381 >= 0, X2381 >= 0, X3189 >= 0, X2 >= 0, z = 1 + (1 + X1381 + X2381 + X3189) + X2 + X3 mark(z) -{ 2 }-> a__U51(a__U51(mark(X1380), X2380, X3188), X2, X3) :|: X2380 >= 0, X3188 >= 0, X1380 >= 0, X3 >= 0, z = 1 + (1 + X1380 + X2380 + X3188) + X2 + X3, X2 >= 0 mark(z) -{ 2 }-> a__U51(a__U41(mark(X1379), X2379), X2, X3) :|: z = 1 + (1 + X1379 + X2379) + X2 + X3, X1379 >= 0, X3 >= 0, X2379 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U51(a__U32(mark(X533)), X2, X3) :|: X3 >= 0, z = 1 + (1 + X533) + X2 + X3, X2 >= 0, X533 >= 0 mark(z) -{ 2 }-> a__U51(a__U31(mark(X1378), X2378), X2, X3) :|: X2378 >= 0, z = 1 + (1 + X1378 + X2378) + X2 + X3, X3 >= 0, X2 >= 0, X1378 >= 0 mark(z) -{ 2 }-> a__U51(a__U21(mark(X532)), X2, X3) :|: z = 1 + (1 + X532) + X2 + X3, X3 >= 0, X532 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U51(a__U12(mark(X530)), X2, X3) :|: X530 >= 0, X3 >= 0, X2 >= 0, z = 1 + (1 + X530) + X2 + X3 mark(z) -{ 2 }-> a__U51(a__U11(mark(X1377), X2377), X2, X3) :|: X2377 >= 0, z = 1 + (1 + X1377 + X2377) + X2 + X3, X3 >= 0, X2 >= 0, X1377 >= 0 mark(z) -{ 2 }-> a__U51(1, X2, X3) :|: z = 1 + 1 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U51(0, X2, X3) :|: z = 1 + 0 + X2 + X3, X3 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U51(1 + mark(X535), X2, X3) :|: X3 >= 0, z = 1 + (1 + X535) + X2 + X3, X2 >= 0, X535 >= 0 mark(z) -{ 2 }-> a__U41(a__x(mark(X1376), mark(X2376)), X2) :|: X1376 >= 0, X2376 >= 0, z = 1 + (1 + X1376 + X2376) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__plus(mark(X1373), mark(X2373)), X2) :|: z = 1 + (1 + X1373 + X2373) + X2, X1373 >= 0, X2 >= 0, X2373 >= 0 mark(z) -{ 2 }-> a__U41(a__isNat(X525), X2) :|: z = 1 + (1 + X525) + X2, X2 >= 0, X525 >= 0 mark(z) -{ 2 }-> a__U41(a__U72(mark(X1375), X2375, X3187), X2) :|: X1375 >= 0, z = 1 + (1 + X1375 + X2375 + X3187) + X2, X2375 >= 0, X3187 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U71(mark(X1374), X2374, X3186), X2) :|: X2374 >= 0, X1374 >= 0, z = 1 + (1 + X1374 + X2374 + X3186) + X2, X3186 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U61(mark(X528)), X2) :|: X528 >= 0, z = 1 + (1 + X528) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U52(mark(X1372), X2372, X3185), X2) :|: X1372 >= 0, X3185 >= 0, z = 1 + (1 + X1372 + X2372 + X3185) + X2, X2 >= 0, X2372 >= 0 mark(z) -{ 2 }-> a__U41(a__U51(mark(X1371), X2371, X3184), X2) :|: X1371 >= 0, z = 1 + (1 + X1371 + X2371 + X3184) + X2, X3184 >= 0, X2371 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U41(mark(X1370), X2370), X2) :|: X2370 >= 0, z = 1 + (1 + X1370 + X2370) + X2, X2 >= 0, X1370 >= 0 mark(z) -{ 2 }-> a__U41(a__U32(mark(X527)), X2) :|: X527 >= 0, X2 >= 0, z = 1 + (1 + X527) + X2 mark(z) -{ 2 }-> a__U41(a__U31(mark(X1369), X2369), X2) :|: X1369 >= 0, z = 1 + (1 + X1369 + X2369) + X2, X2369 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U21(mark(X526)), X2) :|: z = 1 + (1 + X526) + X2, X526 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(a__U12(mark(X524)), X2) :|: X2 >= 0, z = 1 + (1 + X524) + X2, X524 >= 0 mark(z) -{ 2 }-> a__U41(a__U11(mark(X1368), X2368), X2) :|: X2368 >= 0, z = 1 + (1 + X1368 + X2368) + X2, X1368 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U41(1, z - 2) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U41(0, z - 1) :|: z - 1 >= 0 mark(z) -{ 2 }-> a__U41(1 + mark(X529), X2) :|: z = 1 + (1 + X529) + X2, X529 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U32(a__x(mark(X1367), mark(X2367))) :|: z = 1 + (1 + X1367 + X2367), X2367 >= 0, X1367 >= 0 mark(z) -{ 2 }-> a__U32(a__plus(mark(X1364), mark(X2364))) :|: X1364 >= 0, z = 1 + (1 + X1364 + X2364), X2364 >= 0 mark(z) -{ 2 }-> a__U32(a__isNat(z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U32(a__U72(mark(X1366), X2366, X3183)) :|: X2366 >= 0, X3183 >= 0, z = 1 + (1 + X1366 + X2366 + X3183), X1366 >= 0 mark(z) -{ 2 }-> a__U32(a__U71(mark(X1365), X2365, X3182)) :|: X1365 >= 0, X2365 >= 0, X3182 >= 0, z = 1 + (1 + X1365 + X2365 + X3182) mark(z) -{ 2 }-> a__U32(a__U61(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U32(a__U52(mark(X1363), X2363, X3181)) :|: X2363 >= 0, X1363 >= 0, X3181 >= 0, z = 1 + (1 + X1363 + X2363 + X3181) mark(z) -{ 2 }-> a__U32(a__U51(mark(X1362), X2362, X3180)) :|: X1362 >= 0, z = 1 + (1 + X1362 + X2362 + X3180), X2362 >= 0, X3180 >= 0 mark(z) -{ 2 }-> a__U32(a__U41(mark(X1361), X2361)) :|: X1361 >= 0, X2361 >= 0, z = 1 + (1 + X1361 + X2361) mark(z) -{ 2 }-> a__U32(a__U32(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U32(a__U31(mark(X1360), X2360)) :|: X2360 >= 0, X1360 >= 0, z = 1 + (1 + X1360 + X2360) mark(z) -{ 2 }-> a__U32(a__U21(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U32(a__U12(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U32(a__U11(mark(X1359), X2359)) :|: z = 1 + (1 + X1359 + X2359), X1359 >= 0, X2359 >= 0 mark(z) -{ 2 }-> a__U32(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U31(a__x(mark(X1358), mark(X2358)), X2) :|: z = 1 + (1 + X1358 + X2358) + X2, X2358 >= 0, X2 >= 0, X1358 >= 0 mark(z) -{ 2 }-> a__U31(a__plus(mark(X1355), mark(X2355)), X2) :|: X1355 >= 0, z = 1 + (1 + X1355 + X2355) + X2, X2355 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__isNat(X513), X2) :|: X513 >= 0, X2 >= 0, z = 1 + (1 + X513) + X2 mark(z) -{ 2 }-> a__U31(a__U72(mark(X1357), X2357, X3179), X2) :|: z = 1 + (1 + X1357 + X2357 + X3179) + X2, X2357 >= 0, X3179 >= 0, X2 >= 0, X1357 >= 0 mark(z) -{ 2 }-> a__U31(a__U71(mark(X1356), X2356, X3178), X2) :|: X2356 >= 0, X1356 >= 0, X2 >= 0, X3178 >= 0, z = 1 + (1 + X1356 + X2356 + X3178) + X2 mark(z) -{ 2 }-> a__U31(a__U61(mark(X516)), X2) :|: z = 1 + (1 + X516) + X2, X516 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__U52(mark(X1354), X2354, X3177), X2) :|: X1354 >= 0, z = 1 + (1 + X1354 + X2354 + X3177) + X2, X2354 >= 0, X2 >= 0, X3177 >= 0 mark(z) -{ 2 }-> a__U31(a__U51(mark(X1353), X2353, X3176), X2) :|: X1353 >= 0, X3176 >= 0, X2 >= 0, z = 1 + (1 + X1353 + X2353 + X3176) + X2, X2353 >= 0 mark(z) -{ 2 }-> a__U31(a__U41(mark(X1352), X2352), X2) :|: z = 1 + (1 + X1352 + X2352) + X2, X1352 >= 0, X2 >= 0, X2352 >= 0 mark(z) -{ 2 }-> a__U31(a__U32(mark(X515)), X2) :|: z = 1 + (1 + X515) + X2, X515 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__U31(mark(X1351), X2351), X2) :|: X1351 >= 0, z = 1 + (1 + X1351 + X2351) + X2, X2351 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__U21(mark(X514)), X2) :|: z = 1 + (1 + X514) + X2, X2 >= 0, X514 >= 0 mark(z) -{ 2 }-> a__U31(a__U12(mark(X512)), X2) :|: z = 1 + (1 + X512) + X2, X512 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U31(a__U11(mark(X1350), X2350), X2) :|: z = 1 + (1 + X1350 + X2350) + X2, X2350 >= 0, X2 >= 0, X1350 >= 0 mark(z) -{ 2 }-> a__U31(1, z - 2) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U31(0, z - 1) :|: z - 1 >= 0 mark(z) -{ 2 }-> a__U31(1 + mark(X517), X2) :|: X517 >= 0, z = 1 + (1 + X517) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U21(a__x(mark(X1349), mark(X2349))) :|: z = 1 + (1 + X1349 + X2349), X1349 >= 0, X2349 >= 0 mark(z) -{ 2 }-> a__U21(a__plus(mark(X1346), mark(X2346))) :|: X2346 >= 0, X1346 >= 0, z = 1 + (1 + X1346 + X2346) mark(z) -{ 2 }-> a__U21(a__isNat(z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U21(a__U72(mark(X1348), X2348, X3175)) :|: X1348 >= 0, X3175 >= 0, X2348 >= 0, z = 1 + (1 + X1348 + X2348 + X3175) mark(z) -{ 2 }-> a__U21(a__U71(mark(X1347), X2347, X3174)) :|: z = 1 + (1 + X1347 + X2347 + X3174), X2347 >= 0, X3174 >= 0, X1347 >= 0 mark(z) -{ 2 }-> a__U21(a__U61(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U21(a__U52(mark(X1345), X2345, X3173)) :|: z = 1 + (1 + X1345 + X2345 + X3173), X1345 >= 0, X2345 >= 0, X3173 >= 0 mark(z) -{ 2 }-> a__U21(a__U51(mark(X1344), X2344, X3172)) :|: X1344 >= 0, z = 1 + (1 + X1344 + X2344 + X3172), X2344 >= 0, X3172 >= 0 mark(z) -{ 2 }-> a__U21(a__U41(mark(X1343), X2343)) :|: z = 1 + (1 + X1343 + X2343), X1343 >= 0, X2343 >= 0 mark(z) -{ 2 }-> a__U21(a__U32(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U21(a__U31(mark(X1342), X2342)) :|: X2342 >= 0, z = 1 + (1 + X1342 + X2342), X1342 >= 0 mark(z) -{ 2 }-> a__U21(a__U21(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U21(a__U12(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U21(a__U11(mark(X1341), X2341)) :|: z = 1 + (1 + X1341 + X2341), X1341 >= 0, X2341 >= 0 mark(z) -{ 2 }-> a__U21(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U12(a__x(mark(X1340), mark(X2340))) :|: z = 1 + (1 + X1340 + X2340), X2340 >= 0, X1340 >= 0 mark(z) -{ 2 }-> a__U12(a__plus(mark(X1337), mark(X2337))) :|: z = 1 + (1 + X1337 + X2337), X2337 >= 0, X1337 >= 0 mark(z) -{ 2 }-> a__U12(a__isNat(z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U12(a__U72(mark(X1339), X2339, X3171)) :|: X2339 >= 0, X1339 >= 0, z = 1 + (1 + X1339 + X2339 + X3171), X3171 >= 0 mark(z) -{ 2 }-> a__U12(a__U71(mark(X1338), X2338, X3170)) :|: z = 1 + (1 + X1338 + X2338 + X3170), X2338 >= 0, X1338 >= 0, X3170 >= 0 mark(z) -{ 2 }-> a__U12(a__U61(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U12(a__U52(mark(X1336), X2336, X3169)) :|: X2336 >= 0, z = 1 + (1 + X1336 + X2336 + X3169), X3169 >= 0, X1336 >= 0 mark(z) -{ 2 }-> a__U12(a__U51(mark(X1335), X2335, X3168)) :|: X2335 >= 0, z = 1 + (1 + X1335 + X2335 + X3168), X1335 >= 0, X3168 >= 0 mark(z) -{ 2 }-> a__U12(a__U41(mark(X1334), X2334)) :|: z = 1 + (1 + X1334 + X2334), X1334 >= 0, X2334 >= 0 mark(z) -{ 2 }-> a__U12(a__U32(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U12(a__U31(mark(X1333), X2333)) :|: X1333 >= 0, z = 1 + (1 + X1333 + X2333), X2333 >= 0 mark(z) -{ 2 }-> a__U12(a__U21(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U12(a__U12(mark(z - 2))) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U12(a__U11(mark(X1332), X2332)) :|: z = 1 + (1 + X1332 + X2332), X1332 >= 0, X2332 >= 0 mark(z) -{ 2 }-> a__U12(1 + mark(z - 2)) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U11(a__x(mark(X1331), mark(X2331)), X2) :|: X2331 >= 0, z = 1 + (1 + X1331 + X2331) + X2, X2 >= 0, X1331 >= 0 mark(z) -{ 2 }-> a__U11(a__plus(mark(X1328), mark(X2328)), X2) :|: z = 1 + (1 + X1328 + X2328) + X2, X2328 >= 0, X1328 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__isNat(X495), X2) :|: z = 1 + (1 + X495) + X2, X2 >= 0, X495 >= 0 mark(z) -{ 2 }-> a__U11(a__U72(mark(X1330), X2330, X3167), X2) :|: X3167 >= 0, X2330 >= 0, X2 >= 0, z = 1 + (1 + X1330 + X2330 + X3167) + X2, X1330 >= 0 mark(z) -{ 2 }-> a__U11(a__U71(mark(X1329), X2329, X3166), X2) :|: X2329 >= 0, X1329 >= 0, X3166 >= 0, z = 1 + (1 + X1329 + X2329 + X3166) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U61(mark(X498)), X2) :|: X498 >= 0, z = 1 + (1 + X498) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U52(mark(X1327), X2327, X3165), X2) :|: X1327 >= 0, X2327 >= 0, X3165 >= 0, z = 1 + (1 + X1327 + X2327 + X3165) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U51(mark(X1326), X2326, X3164), X2) :|: X2326 >= 0, X3164 >= 0, X1326 >= 0, X2 >= 0, z = 1 + (1 + X1326 + X2326 + X3164) + X2 mark(z) -{ 2 }-> a__U11(a__U41(mark(X1325), X2325), X2) :|: X2325 >= 0, z = 1 + (1 + X1325 + X2325) + X2, X1325 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U32(mark(X497)), X2) :|: z = 1 + (1 + X497) + X2, X497 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U31(mark(X1324), X2324), X2) :|: X1324 >= 0, z = 1 + (1 + X1324 + X2324) + X2, X2324 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U21(mark(X496)), X2) :|: z = 1 + (1 + X496) + X2, X496 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U12(mark(X494)), X2) :|: X494 >= 0, z = 1 + (1 + X494) + X2, X2 >= 0 mark(z) -{ 2 }-> a__U11(a__U11(mark(X1323), X2323), X2) :|: X1323 >= 0, z = 1 + (1 + X1323 + X2323) + X2, X2323 >= 0, X2 >= 0 mark(z) -{ 2 }-> a__U11(1, z - 2) :|: z - 2 >= 0 mark(z) -{ 2 }-> a__U11(0, z - 1) :|: z - 1 >= 0 mark(z) -{ 2 }-> a__U11(1 + mark(X499), X2) :|: X499 >= 0, X2 >= 0, z = 1 + (1 + X499) + X2 mark(z) -{ 1 }-> 1 :|: z = 1 mark(z) -{ 3 }-> 1 :|: z = 1 + 1, 1 = 1 mark(z) -{ 1 }-> 0 :|: z = 0 mark(z) -{ 3 }-> 0 :|: z = 1 + 1, 1 = 1 mark(z) -{ 3 }-> 1 + X :|: z = 1 + 1, X >= 0, 1 = X mark(z) -{ 3 }-> 1 + X :|: z = 1 + 0, X >= 0, 0 = X mark(z) -{ 1 }-> 1 + mark(z - 1) :|: z - 1 >= 0 ---------------------------------------- (37) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS with rewrite strategy PARALLEL_INNERMOST to CDT ---------------------------------------- (38) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(A__U12(a__isNat(z0)), A__ISNAT(z0)) A__U11(z0, z1) -> c1 A__U12(tt) -> c2 A__U12(z0) -> c3 A__U21(tt) -> c4 A__U21(z0) -> c5 A__U31(tt, z0) -> c6(A__U32(a__isNat(z0)), A__ISNAT(z0)) A__U31(z0, z1) -> c7 A__U32(tt) -> c8 A__U32(z0) -> c9 A__U41(tt, z0) -> c10(MARK(z0)) A__U41(z0, z1) -> c11 A__U51(tt, z0, z1) -> c12(A__U52(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U51(z0, z1, z2) -> c13 A__U52(tt, z0, z1) -> c14(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U52(tt, z0, z1) -> c15(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U52(z0, z1, z2) -> c16 A__U61(tt) -> c17 A__U61(z0) -> c18 A__U71(tt, z0, z1) -> c19(A__U72(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U71(z0, z1, z2) -> c20 A__U72(tt, z0, z1) -> c21(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) A__U72(tt, z0, z1) -> c22(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) A__U72(z0, z1, z2) -> c24 A__ISNAT(0) -> c25 A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__U21(a__isNat(z0)), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(z0) -> c29 A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__PLUS(z0, z1) -> c32 A__X(z0, 0) -> c33(A__U61(a__isNat(z0)), A__ISNAT(z0)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, z1) -> c35 MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c37(A__U12(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U21(z0)) -> c39(A__U21(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U32(z0)) -> c41(A__U32(mark(z0)), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U61(z0)) -> c47(A__U61(mark(z0)), MARK(z0)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c52 MARK(s(z0)) -> c53(MARK(z0)) MARK(0) -> c54 S tuples: A__U11(tt, z0) -> c(A__U12(a__isNat(z0)), A__ISNAT(z0)) A__U11(z0, z1) -> c1 A__U12(tt) -> c2 A__U12(z0) -> c3 A__U21(tt) -> c4 A__U21(z0) -> c5 A__U31(tt, z0) -> c6(A__U32(a__isNat(z0)), A__ISNAT(z0)) A__U31(z0, z1) -> c7 A__U32(tt) -> c8 A__U32(z0) -> c9 A__U41(tt, z0) -> c10(MARK(z0)) A__U41(z0, z1) -> c11 A__U51(tt, z0, z1) -> c12(A__U52(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U51(z0, z1, z2) -> c13 A__U52(tt, z0, z1) -> c14(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U52(tt, z0, z1) -> c15(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U52(z0, z1, z2) -> c16 A__U61(tt) -> c17 A__U61(z0) -> c18 A__U71(tt, z0, z1) -> c19(A__U72(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U71(z0, z1, z2) -> c20 A__U72(tt, z0, z1) -> c21(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) A__U72(tt, z0, z1) -> c22(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) A__U72(z0, z1, z2) -> c24 A__ISNAT(0) -> c25 A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__U21(a__isNat(z0)), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(z0) -> c29 A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__PLUS(z0, z1) -> c32 A__X(z0, 0) -> c33(A__U61(a__isNat(z0)), A__ISNAT(z0)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, z1) -> c35 MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c37(A__U12(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U21(z0)) -> c39(A__U21(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U32(z0)) -> c41(A__U32(mark(z0)), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U61(z0)) -> c47(A__U61(mark(z0)), MARK(z0)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(tt) -> c52 MARK(s(z0)) -> c53(MARK(z0)) MARK(0) -> c54 K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U11_2, A__U12_1, A__U21_1, A__U31_2, A__U32_1, A__U41_2, A__U51_3, A__U52_3, A__U61_1, A__U71_3, A__U72_3, A__ISNAT_1, A__PLUS_2, A__X_2, MARK_1 Compound Symbols: c_2, c1, c2, c3, c4, c5, c6_2, c7, c8, c9, c10_1, c11, c12_2, c13, c14_2, c15_2, c16, c17, c18, c19_2, c20, c21_3, c22_3, c23_2, c24, c25, c26_2, c27_2, c28_2, c29, c30_2, c31_2, c32, c33_2, c34_2, c35, c36_2, c37_2, c38_1, c39_2, c40_2, c41_2, c42_2, c43_2, c44_2, c45_2, c46_2, c47_2, c48_2, c49_2, c50_2, c51_2, c52, c53_1, c54 ---------------------------------------- (39) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 21 trailing nodes: A__U32(tt) -> c8 A__U21(z0) -> c5 A__U71(z0, z1, z2) -> c20 MARK(0) -> c54 A__U52(z0, z1, z2) -> c16 A__U41(z0, z1) -> c11 A__U31(z0, z1) -> c7 A__U12(tt) -> c2 A__PLUS(z0, z1) -> c32 A__U51(z0, z1, z2) -> c13 A__U61(tt) -> c17 A__U12(z0) -> c3 A__U11(z0, z1) -> c1 A__ISNAT(z0) -> c29 A__ISNAT(0) -> c25 A__U72(z0, z1, z2) -> c24 A__U61(z0) -> c18 MARK(tt) -> c52 A__U32(z0) -> c9 A__X(z0, z1) -> c35 A__U21(tt) -> c4 ---------------------------------------- (40) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U11(tt, z0) -> c(A__U12(a__isNat(z0)), A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__U32(a__isNat(z0)), A__ISNAT(z0)) A__U41(tt, z0) -> c10(MARK(z0)) A__U51(tt, z0, z1) -> c12(A__U52(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U52(tt, z0, z1) -> c14(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U52(tt, z0, z1) -> c15(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U71(tt, z0, z1) -> c19(A__U72(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U72(tt, z0, z1) -> c21(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) A__U72(tt, z0, z1) -> c22(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__U21(a__isNat(z0)), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, 0) -> c33(A__U61(a__isNat(z0)), A__ISNAT(z0)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c37(A__U12(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U21(z0)) -> c39(A__U21(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U32(z0)) -> c41(A__U32(mark(z0)), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U61(z0)) -> c47(A__U61(mark(z0)), MARK(z0)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) S tuples: A__U11(tt, z0) -> c(A__U12(a__isNat(z0)), A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__U32(a__isNat(z0)), A__ISNAT(z0)) A__U41(tt, z0) -> c10(MARK(z0)) A__U51(tt, z0, z1) -> c12(A__U52(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U52(tt, z0, z1) -> c14(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U52(tt, z0, z1) -> c15(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U71(tt, z0, z1) -> c19(A__U72(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U72(tt, z0, z1) -> c21(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) A__U72(tt, z0, z1) -> c22(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__U21(a__isNat(z0)), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, 0) -> c33(A__U61(a__isNat(z0)), A__ISNAT(z0)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(U12(z0)) -> c37(A__U12(mark(z0)), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U21(z0)) -> c39(A__U21(mark(z0)), MARK(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U32(z0)) -> c41(A__U32(mark(z0)), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U61(z0)) -> c47(A__U61(mark(z0)), MARK(z0)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U11_2, A__U31_2, A__U41_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__ISNAT_1, A__PLUS_2, A__X_2, MARK_1 Compound Symbols: c_2, c6_2, c10_1, c12_2, c14_2, c15_2, c19_2, c21_3, c22_3, c23_2, c26_2, c27_2, c28_2, c30_2, c31_2, c33_2, c34_2, c36_2, c37_2, c38_1, c39_2, c40_2, c41_2, c42_2, c43_2, c44_2, c45_2, c46_2, c47_2, c48_2, c49_2, c50_2, c51_2, c53_1 ---------------------------------------- (41) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 8 trailing tuple parts ---------------------------------------- (42) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__U51(tt, z0, z1) -> c12(A__U52(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U52(tt, z0, z1) -> c14(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U52(tt, z0, z1) -> c15(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U71(tt, z0, z1) -> c19(A__U72(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U72(tt, z0, z1) -> c21(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) A__U72(tt, z0, z1) -> c22(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__U51(tt, z0, z1) -> c12(A__U52(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U52(tt, z0, z1) -> c14(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U52(tt, z0, z1) -> c15(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U71(tt, z0, z1) -> c19(A__U72(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U72(tt, z0, z1) -> c21(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) A__U72(tt, z0, z1) -> c22(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__ISNAT_1, A__PLUS_2, A__X_2, MARK_1, A__U11_2, A__U31_2 Compound Symbols: c10_1, c12_2, c14_2, c15_2, c19_2, c21_3, c22_3, c23_2, c26_2, c28_2, c30_2, c31_2, c34_2, c36_2, c38_1, c40_2, c42_2, c43_2, c44_2, c45_2, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1 ---------------------------------------- (43) CdtToCpxRelTrsProof (BOTH BOUNDS(ID, ID)) Converted S to standard rules, and D \ S as well as R to relative rules. ---------------------------------------- (44) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__U41(tt, z0) -> c10(MARK(z0)) A__U51(tt, z0, z1) -> c12(A__U52(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U52(tt, z0, z1) -> c14(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U52(tt, z0, z1) -> c15(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U71(tt, z0, z1) -> c19(A__U72(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U72(tt, z0, z1) -> c21(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) A__U72(tt, z0, z1) -> c22(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) The (relative) TRS S consists of the following rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Rewrite Strategy: INNERMOST ---------------------------------------- (45) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS ---------------------------------------- (46) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__U41(tt, z0) -> c10(MARK(z0)) A__U51(tt, z0, z1) -> c12(A__U52(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U52(tt, z0, z1) -> c14(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U52(tt, z0, z1) -> c15(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U71(tt, z0, z1) -> c19(A__U72(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U72(tt, z0, z1) -> c21(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) A__U72(tt, z0, z1) -> c22(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (47) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (48) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, INF). The TRS R consists of the following rules: A__U41(tt, z0) -> c10(MARK(z0)) [1] A__U51(tt, z0, z1) -> c12(A__U52(a__isNat(z1), z0, z1), A__ISNAT(z1)) [1] A__U52(tt, z0, z1) -> c14(A__PLUS(mark(z1), mark(z0)), MARK(z1)) [1] A__U52(tt, z0, z1) -> c15(A__PLUS(mark(z1), mark(z0)), MARK(z0)) [1] A__U71(tt, z0, z1) -> c19(A__U72(a__isNat(z1), z0, z1), A__ISNAT(z1)) [1] A__U72(tt, z0, z1) -> c21(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) [1] A__U72(tt, z0, z1) -> c22(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) [1] A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) [1] A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) [1] A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) [1] A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) [1] A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) [1] A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) [1] MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) [1] MARK(isNat(z0)) -> c38(A__ISNAT(z0)) [1] MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) [1] MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) [1] MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) [1] MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) [1] MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1] MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1] MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) [1] MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) [1] MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) [1] MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) [1] MARK(s(z0)) -> c53(MARK(z0)) [1] A__U11(tt, z0) -> c(A__ISNAT(z0)) [1] A__U31(tt, z0) -> c6(A__ISNAT(z0)) [1] A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) [1] A__X(z0, 0) -> c33(A__ISNAT(z0)) [1] MARK(U12(z0)) -> c37(MARK(z0)) [1] MARK(U21(z0)) -> c39(MARK(z0)) [1] MARK(U32(z0)) -> c41(MARK(z0)) [1] MARK(U61(z0)) -> c47(MARK(z0)) [1] a__U11(tt, z0) -> a__U12(a__isNat(z0)) [0] a__U11(z0, z1) -> U11(z0, z1) [0] a__U12(tt) -> tt [0] a__U12(z0) -> U12(z0) [0] a__U21(tt) -> tt [0] a__U21(z0) -> U21(z0) [0] a__U31(tt, z0) -> a__U32(a__isNat(z0)) [0] a__U31(z0, z1) -> U31(z0, z1) [0] a__U32(tt) -> tt [0] a__U32(z0) -> U32(z0) [0] a__U41(tt, z0) -> mark(z0) [0] a__U41(z0, z1) -> U41(z0, z1) [0] a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) [0] a__U51(z0, z1, z2) -> U51(z0, z1, z2) [0] a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) [0] a__U52(z0, z1, z2) -> U52(z0, z1, z2) [0] a__U61(tt) -> 0 [0] a__U61(z0) -> U61(z0) [0] a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) [0] a__U71(z0, z1, z2) -> U71(z0, z1, z2) [0] a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) [0] a__U72(z0, z1, z2) -> U72(z0, z1, z2) [0] a__isNat(0) -> tt [0] a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) [0] a__isNat(s(z0)) -> a__U21(a__isNat(z0)) [0] a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) [0] a__isNat(z0) -> isNat(z0) [0] a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) [0] a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) [0] a__plus(z0, z1) -> plus(z0, z1) [0] a__x(z0, 0) -> a__U61(a__isNat(z0)) [0] a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) [0] a__x(z0, z1) -> x(z0, z1) [0] mark(U11(z0, z1)) -> a__U11(mark(z0), z1) [0] mark(U12(z0)) -> a__U12(mark(z0)) [0] mark(isNat(z0)) -> a__isNat(z0) [0] mark(U21(z0)) -> a__U21(mark(z0)) [0] mark(U31(z0, z1)) -> a__U31(mark(z0), z1) [0] mark(U32(z0)) -> a__U32(mark(z0)) [0] mark(U41(z0, z1)) -> a__U41(mark(z0), z1) [0] mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) [0] mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) [0] mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) [0] mark(U61(z0)) -> a__U61(mark(z0)) [0] mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) [0] mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) [0] mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) [0] mark(tt) -> tt [0] mark(s(z0)) -> s(mark(z0)) [0] mark(0) -> 0 [0] Rewrite Strategy: INNERMOST ---------------------------------------- (49) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (50) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: A__U41(tt, z0) -> c10(MARK(z0)) [1] A__U51(tt, z0, z1) -> c12(A__U52(a__isNat(z1), z0, z1), A__ISNAT(z1)) [1] A__U52(tt, z0, z1) -> c14(A__PLUS(mark(z1), mark(z0)), MARK(z1)) [1] A__U52(tt, z0, z1) -> c15(A__PLUS(mark(z1), mark(z0)), MARK(z0)) [1] A__U71(tt, z0, z1) -> c19(A__U72(a__isNat(z1), z0, z1), A__ISNAT(z1)) [1] A__U72(tt, z0, z1) -> c21(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) [1] A__U72(tt, z0, z1) -> c22(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) [1] A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) [1] A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) [1] A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) [1] A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) [1] A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) [1] A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) [1] MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) [1] MARK(isNat(z0)) -> c38(A__ISNAT(z0)) [1] MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) [1] MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) [1] MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) [1] MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) [1] MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1] MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1] MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) [1] MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) [1] MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) [1] MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) [1] MARK(s(z0)) -> c53(MARK(z0)) [1] A__U11(tt, z0) -> c(A__ISNAT(z0)) [1] A__U31(tt, z0) -> c6(A__ISNAT(z0)) [1] A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) [1] A__X(z0, 0) -> c33(A__ISNAT(z0)) [1] MARK(U12(z0)) -> c37(MARK(z0)) [1] MARK(U21(z0)) -> c39(MARK(z0)) [1] MARK(U32(z0)) -> c41(MARK(z0)) [1] MARK(U61(z0)) -> c47(MARK(z0)) [1] a__U11(tt, z0) -> a__U12(a__isNat(z0)) [0] a__U11(z0, z1) -> U11(z0, z1) [0] a__U12(tt) -> tt [0] a__U12(z0) -> U12(z0) [0] a__U21(tt) -> tt [0] a__U21(z0) -> U21(z0) [0] a__U31(tt, z0) -> a__U32(a__isNat(z0)) [0] a__U31(z0, z1) -> U31(z0, z1) [0] a__U32(tt) -> tt [0] a__U32(z0) -> U32(z0) [0] a__U41(tt, z0) -> mark(z0) [0] a__U41(z0, z1) -> U41(z0, z1) [0] a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) [0] a__U51(z0, z1, z2) -> U51(z0, z1, z2) [0] a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) [0] a__U52(z0, z1, z2) -> U52(z0, z1, z2) [0] a__U61(tt) -> 0 [0] a__U61(z0) -> U61(z0) [0] a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) [0] a__U71(z0, z1, z2) -> U71(z0, z1, z2) [0] a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) [0] a__U72(z0, z1, z2) -> U72(z0, z1, z2) [0] a__isNat(0) -> tt [0] a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) [0] a__isNat(s(z0)) -> a__U21(a__isNat(z0)) [0] a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) [0] a__isNat(z0) -> isNat(z0) [0] a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) [0] a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) [0] a__plus(z0, z1) -> plus(z0, z1) [0] a__x(z0, 0) -> a__U61(a__isNat(z0)) [0] a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) [0] a__x(z0, z1) -> x(z0, z1) [0] mark(U11(z0, z1)) -> a__U11(mark(z0), z1) [0] mark(U12(z0)) -> a__U12(mark(z0)) [0] mark(isNat(z0)) -> a__isNat(z0) [0] mark(U21(z0)) -> a__U21(mark(z0)) [0] mark(U31(z0, z1)) -> a__U31(mark(z0), z1) [0] mark(U32(z0)) -> a__U32(mark(z0)) [0] mark(U41(z0, z1)) -> a__U41(mark(z0), z1) [0] mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) [0] mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) [0] mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) [0] mark(U61(z0)) -> a__U61(mark(z0)) [0] mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) [0] mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) [0] mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) [0] mark(tt) -> tt [0] mark(s(z0)) -> s(mark(z0)) [0] mark(0) -> 0 [0] The TRS has the following type information: A__U41 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> c10 tt :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 c10 :: c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 -> c10 MARK :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 A__U51 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> c12 c12 :: c14:c15 -> c26:c28:c27 -> c12 A__U52 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> c14:c15 a__isNat :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 A__ISNAT :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> c26:c28:c27 c14 :: c30:c31 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 -> c14:c15 A__PLUS :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> c30:c31 mark :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 c15 :: c30:c31 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 -> c14:c15 A__U71 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> c19 c19 :: c21:c22:c23 -> c26:c28:c27 -> c19 A__U72 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> c21:c22:c23 c21 :: c30:c31 -> c34:c33 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 -> c21:c22:c23 a__x :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 A__X :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> c34:c33 c22 :: c30:c31 -> c34:c33 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 -> c21:c22:c23 c23 :: c30:c31 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 -> c21:c22:c23 plus :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 c26 :: c -> c26:c28:c27 -> c26:c28:c27 A__U11 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> c x :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 c28 :: c6 -> c26:c28:c27 -> c26:c28:c27 A__U31 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> c6 0 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 c30 :: c10 -> c26:c28:c27 -> c30:c31 s :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 c31 :: c12 -> c26:c28:c27 -> c30:c31 c34 :: c19 -> c26:c28:c27 -> c34:c33 U11 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 c36 :: c -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 isNat :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 c38 :: c26:c28:c27 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 U31 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 c40 :: c6 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 U41 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 c42 :: c10 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 U51 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 c43 :: c12 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 U52 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 c44 :: c14:c15 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 c45 :: c30:c31 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 c46 :: c30:c31 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 U71 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 c48 :: c19 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 U72 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 c49 :: c21:c22:c23 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 c50 :: c34:c33 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 c51 :: c34:c33 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 c53 :: c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 c :: c26:c28:c27 -> c c6 :: c26:c28:c27 -> c6 c27 :: c26:c28:c27 -> c26:c28:c27 c33 :: c26:c28:c27 -> c34:c33 U12 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 c37 :: c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 U21 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 c39 :: c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 U32 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 c41 :: c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 U61 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 c47 :: c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 a__U11 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 a__U12 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 a__U21 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 a__U31 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 a__U32 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 a__U41 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 a__U51 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 a__U52 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 a__plus :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 a__U61 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 a__U71 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 a__U72 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61 Rewrite Strategy: INNERMOST ---------------------------------------- (51) CompletionProof (UPPER BOUND(ID)) The transformation into a RNTS is sound, since: (a) The obligation is a constructor system where every type has a constant constructor, (b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols: A__U41_2 A__U51_3 A__U52_3 A__U71_3 A__U72_3 A__ISNAT_1 A__PLUS_2 A__X_2 MARK_1 A__U11_2 A__U31_2 (c) The following functions are completely defined: a__U11_2 a__U12_1 a__U21_1 a__U31_2 a__U32_1 a__U41_2 a__U51_3 a__U52_3 a__U61_1 a__U71_3 a__U72_3 a__isNat_1 a__plus_2 a__x_2 mark_1 Due to the following rules being added: a__U11(v0, v1) -> null_a__U11 [0] a__U12(v0) -> null_a__U12 [0] a__U21(v0) -> null_a__U21 [0] a__U31(v0, v1) -> null_a__U31 [0] a__U32(v0) -> null_a__U32 [0] a__U41(v0, v1) -> null_a__U41 [0] a__U51(v0, v1, v2) -> null_a__U51 [0] a__U52(v0, v1, v2) -> null_a__U52 [0] a__U61(v0) -> null_a__U61 [0] a__U71(v0, v1, v2) -> null_a__U71 [0] a__U72(v0, v1, v2) -> null_a__U72 [0] a__isNat(v0) -> null_a__isNat [0] a__plus(v0, v1) -> null_a__plus [0] a__x(v0, v1) -> null_a__x [0] mark(v0) -> null_mark [0] And the following fresh constants: null_a__U11, null_a__U12, null_a__U21, null_a__U31, null_a__U32, null_a__U41, null_a__U51, null_a__U52, null_a__U61, null_a__U71, null_a__U72, null_a__isNat, null_a__plus, null_a__x, null_mark, const, const1, const2, const3, const4, const5, const6, const7, const8, const9, const10 ---------------------------------------- (52) Obligation: Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: A__U41(tt, z0) -> c10(MARK(z0)) [1] A__U51(tt, z0, z1) -> c12(A__U52(a__isNat(z1), z0, z1), A__ISNAT(z1)) [1] A__U52(tt, z0, z1) -> c14(A__PLUS(mark(z1), mark(z0)), MARK(z1)) [1] A__U52(tt, z0, z1) -> c15(A__PLUS(mark(z1), mark(z0)), MARK(z0)) [1] A__U71(tt, z0, z1) -> c19(A__U72(a__isNat(z1), z0, z1), A__ISNAT(z1)) [1] A__U72(tt, z0, z1) -> c21(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) [1] A__U72(tt, z0, z1) -> c22(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) [1] A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) [1] A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) [1] A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) [1] A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) [1] A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) [1] A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) [1] MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) [1] MARK(isNat(z0)) -> c38(A__ISNAT(z0)) [1] MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) [1] MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) [1] MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) [1] MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) [1] MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1] MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1] MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) [1] MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) [1] MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) [1] MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) [1] MARK(s(z0)) -> c53(MARK(z0)) [1] A__U11(tt, z0) -> c(A__ISNAT(z0)) [1] A__U31(tt, z0) -> c6(A__ISNAT(z0)) [1] A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) [1] A__X(z0, 0) -> c33(A__ISNAT(z0)) [1] MARK(U12(z0)) -> c37(MARK(z0)) [1] MARK(U21(z0)) -> c39(MARK(z0)) [1] MARK(U32(z0)) -> c41(MARK(z0)) [1] MARK(U61(z0)) -> c47(MARK(z0)) [1] a__U11(tt, z0) -> a__U12(a__isNat(z0)) [0] a__U11(z0, z1) -> U11(z0, z1) [0] a__U12(tt) -> tt [0] a__U12(z0) -> U12(z0) [0] a__U21(tt) -> tt [0] a__U21(z0) -> U21(z0) [0] a__U31(tt, z0) -> a__U32(a__isNat(z0)) [0] a__U31(z0, z1) -> U31(z0, z1) [0] a__U32(tt) -> tt [0] a__U32(z0) -> U32(z0) [0] a__U41(tt, z0) -> mark(z0) [0] a__U41(z0, z1) -> U41(z0, z1) [0] a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) [0] a__U51(z0, z1, z2) -> U51(z0, z1, z2) [0] a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) [0] a__U52(z0, z1, z2) -> U52(z0, z1, z2) [0] a__U61(tt) -> 0 [0] a__U61(z0) -> U61(z0) [0] a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) [0] a__U71(z0, z1, z2) -> U71(z0, z1, z2) [0] a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) [0] a__U72(z0, z1, z2) -> U72(z0, z1, z2) [0] a__isNat(0) -> tt [0] a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) [0] a__isNat(s(z0)) -> a__U21(a__isNat(z0)) [0] a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) [0] a__isNat(z0) -> isNat(z0) [0] a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) [0] a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) [0] a__plus(z0, z1) -> plus(z0, z1) [0] a__x(z0, 0) -> a__U61(a__isNat(z0)) [0] a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) [0] a__x(z0, z1) -> x(z0, z1) [0] mark(U11(z0, z1)) -> a__U11(mark(z0), z1) [0] mark(U12(z0)) -> a__U12(mark(z0)) [0] mark(isNat(z0)) -> a__isNat(z0) [0] mark(U21(z0)) -> a__U21(mark(z0)) [0] mark(U31(z0, z1)) -> a__U31(mark(z0), z1) [0] mark(U32(z0)) -> a__U32(mark(z0)) [0] mark(U41(z0, z1)) -> a__U41(mark(z0), z1) [0] mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) [0] mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) [0] mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) [0] mark(U61(z0)) -> a__U61(mark(z0)) [0] mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) [0] mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) [0] mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) [0] mark(tt) -> tt [0] mark(s(z0)) -> s(mark(z0)) [0] mark(0) -> 0 [0] a__U11(v0, v1) -> null_a__U11 [0] a__U12(v0) -> null_a__U12 [0] a__U21(v0) -> null_a__U21 [0] a__U31(v0, v1) -> null_a__U31 [0] a__U32(v0) -> null_a__U32 [0] a__U41(v0, v1) -> null_a__U41 [0] a__U51(v0, v1, v2) -> null_a__U51 [0] a__U52(v0, v1, v2) -> null_a__U52 [0] a__U61(v0) -> null_a__U61 [0] a__U71(v0, v1, v2) -> null_a__U71 [0] a__U72(v0, v1, v2) -> null_a__U72 [0] a__isNat(v0) -> null_a__isNat [0] a__plus(v0, v1) -> null_a__plus [0] a__x(v0, v1) -> null_a__x [0] mark(v0) -> null_mark [0] The TRS has the following type information: A__U41 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> c10 tt :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark c10 :: c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 -> c10 MARK :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 A__U51 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> c12 c12 :: c14:c15 -> c26:c28:c27 -> c12 A__U52 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> c14:c15 a__isNat :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark A__ISNAT :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> c26:c28:c27 c14 :: c30:c31 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 -> c14:c15 A__PLUS :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> c30:c31 mark :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark c15 :: c30:c31 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 -> c14:c15 A__U71 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> c19 c19 :: c21:c22:c23 -> c26:c28:c27 -> c19 A__U72 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> c21:c22:c23 c21 :: c30:c31 -> c34:c33 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 -> c21:c22:c23 a__x :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark A__X :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> c34:c33 c22 :: c30:c31 -> c34:c33 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 -> c21:c22:c23 c23 :: c30:c31 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 -> c21:c22:c23 plus :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark c26 :: c -> c26:c28:c27 -> c26:c28:c27 A__U11 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> c x :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark c28 :: c6 -> c26:c28:c27 -> c26:c28:c27 A__U31 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> c6 0 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark c30 :: c10 -> c26:c28:c27 -> c30:c31 s :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark c31 :: c12 -> c26:c28:c27 -> c30:c31 c34 :: c19 -> c26:c28:c27 -> c34:c33 U11 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark c36 :: c -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 isNat :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark c38 :: c26:c28:c27 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 U31 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark c40 :: c6 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 U41 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark c42 :: c10 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 U51 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark c43 :: c12 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 U52 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark c44 :: c14:c15 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 c45 :: c30:c31 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 c46 :: c30:c31 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 U71 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark c48 :: c19 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 U72 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark c49 :: c21:c22:c23 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 c50 :: c34:c33 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 c51 :: c34:c33 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 c53 :: c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 c :: c26:c28:c27 -> c c6 :: c26:c28:c27 -> c6 c27 :: c26:c28:c27 -> c26:c28:c27 c33 :: c26:c28:c27 -> c34:c33 U12 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark c37 :: c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 U21 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark c39 :: c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 U32 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark c41 :: c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 U61 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark c47 :: c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 a__U11 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark a__U12 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark a__U21 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark a__U31 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark a__U32 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark a__U41 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark a__U51 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark a__U52 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark a__plus :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark a__U61 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark a__U71 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark a__U72 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark null_a__U11 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark null_a__U12 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark null_a__U21 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark null_a__U31 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark null_a__U32 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark null_a__U41 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark null_a__U51 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark null_a__U52 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark null_a__U61 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark null_a__U71 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark null_a__U72 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark null_a__isNat :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark null_a__plus :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark null_a__x :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark null_mark :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark const :: c10 const1 :: c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47 const2 :: c12 const3 :: c14:c15 const4 :: c26:c28:c27 const5 :: c30:c31 const6 :: c19 const7 :: c21:c22:c23 const8 :: c34:c33 const9 :: c const10 :: c6 Rewrite Strategy: INNERMOST ---------------------------------------- (53) CompletionProof (UPPER BOUND(ID)) The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: a__U11(v0, v1) -> null_a__U11 [0] a__U12(v0) -> null_a__U12 [0] a__U21(v0) -> null_a__U21 [0] a__U31(v0, v1) -> null_a__U31 [0] a__U32(v0) -> null_a__U32 [0] a__U41(v0, v1) -> null_a__U41 [0] a__U51(v0, v1, v2) -> null_a__U51 [0] a__U52(v0, v1, v2) -> null_a__U52 [0] a__U61(v0) -> null_a__U61 [0] a__U71(v0, v1, v2) -> null_a__U71 [0] a__U72(v0, v1, v2) -> null_a__U72 [0] a__isNat(v0) -> null_a__isNat [0] a__plus(v0, v1) -> null_a__plus [0] a__x(v0, v1) -> null_a__x [0] mark(v0) -> null_mark [0] A__U41(v0, v1) -> null_A__U41 [0] A__U51(v0, v1, v2) -> null_A__U51 [0] A__U52(v0, v1, v2) -> null_A__U52 [0] A__U71(v0, v1, v2) -> null_A__U71 [0] A__U72(v0, v1, v2) -> null_A__U72 [0] A__ISNAT(v0) -> null_A__ISNAT [0] A__PLUS(v0, v1) -> null_A__PLUS [0] A__X(v0, v1) -> null_A__X [0] MARK(v0) -> null_MARK [0] A__U11(v0, v1) -> null_A__U11 [0] A__U31(v0, v1) -> null_A__U31 [0] And the following fresh constants: null_a__U11, null_a__U12, null_a__U21, null_a__U31, null_a__U32, null_a__U41, null_a__U51, null_a__U52, null_a__U61, null_a__U71, null_a__U72, null_a__isNat, null_a__plus, null_a__x, null_mark, null_A__U41, null_A__U51, null_A__U52, null_A__U71, null_A__U72, null_A__ISNAT, null_A__PLUS, null_A__X, null_MARK, null_A__U11, null_A__U31 ---------------------------------------- (54) Obligation: Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: A__U41(tt, z0) -> c10(MARK(z0)) [1] A__U51(tt, z0, z1) -> c12(A__U52(a__isNat(z1), z0, z1), A__ISNAT(z1)) [1] A__U52(tt, z0, z1) -> c14(A__PLUS(mark(z1), mark(z0)), MARK(z1)) [1] A__U52(tt, z0, z1) -> c15(A__PLUS(mark(z1), mark(z0)), MARK(z0)) [1] A__U71(tt, z0, z1) -> c19(A__U72(a__isNat(z1), z0, z1), A__ISNAT(z1)) [1] A__U72(tt, z0, z1) -> c21(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) [1] A__U72(tt, z0, z1) -> c22(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) [1] A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) [1] A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) [1] A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) [1] A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) [1] A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) [1] A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) [1] MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) [1] MARK(isNat(z0)) -> c38(A__ISNAT(z0)) [1] MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) [1] MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) [1] MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) [1] MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) [1] MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) [1] MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) [1] MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) [1] MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) [1] MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) [1] MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) [1] MARK(s(z0)) -> c53(MARK(z0)) [1] A__U11(tt, z0) -> c(A__ISNAT(z0)) [1] A__U31(tt, z0) -> c6(A__ISNAT(z0)) [1] A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) [1] A__X(z0, 0) -> c33(A__ISNAT(z0)) [1] MARK(U12(z0)) -> c37(MARK(z0)) [1] MARK(U21(z0)) -> c39(MARK(z0)) [1] MARK(U32(z0)) -> c41(MARK(z0)) [1] MARK(U61(z0)) -> c47(MARK(z0)) [1] a__U11(tt, z0) -> a__U12(a__isNat(z0)) [0] a__U11(z0, z1) -> U11(z0, z1) [0] a__U12(tt) -> tt [0] a__U12(z0) -> U12(z0) [0] a__U21(tt) -> tt [0] a__U21(z0) -> U21(z0) [0] a__U31(tt, z0) -> a__U32(a__isNat(z0)) [0] a__U31(z0, z1) -> U31(z0, z1) [0] a__U32(tt) -> tt [0] a__U32(z0) -> U32(z0) [0] a__U41(tt, z0) -> mark(z0) [0] a__U41(z0, z1) -> U41(z0, z1) [0] a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) [0] a__U51(z0, z1, z2) -> U51(z0, z1, z2) [0] a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) [0] a__U52(z0, z1, z2) -> U52(z0, z1, z2) [0] a__U61(tt) -> 0 [0] a__U61(z0) -> U61(z0) [0] a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) [0] a__U71(z0, z1, z2) -> U71(z0, z1, z2) [0] a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) [0] a__U72(z0, z1, z2) -> U72(z0, z1, z2) [0] a__isNat(0) -> tt [0] a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) [0] a__isNat(s(z0)) -> a__U21(a__isNat(z0)) [0] a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) [0] a__isNat(z0) -> isNat(z0) [0] a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) [0] a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) [0] a__plus(z0, z1) -> plus(z0, z1) [0] a__x(z0, 0) -> a__U61(a__isNat(z0)) [0] a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) [0] a__x(z0, z1) -> x(z0, z1) [0] mark(U11(z0, z1)) -> a__U11(mark(z0), z1) [0] mark(U12(z0)) -> a__U12(mark(z0)) [0] mark(isNat(z0)) -> a__isNat(z0) [0] mark(U21(z0)) -> a__U21(mark(z0)) [0] mark(U31(z0, z1)) -> a__U31(mark(z0), z1) [0] mark(U32(z0)) -> a__U32(mark(z0)) [0] mark(U41(z0, z1)) -> a__U41(mark(z0), z1) [0] mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) [0] mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) [0] mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) [0] mark(U61(z0)) -> a__U61(mark(z0)) [0] mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) [0] mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) [0] mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) [0] mark(tt) -> tt [0] mark(s(z0)) -> s(mark(z0)) [0] mark(0) -> 0 [0] a__U11(v0, v1) -> null_a__U11 [0] a__U12(v0) -> null_a__U12 [0] a__U21(v0) -> null_a__U21 [0] a__U31(v0, v1) -> null_a__U31 [0] a__U32(v0) -> null_a__U32 [0] a__U41(v0, v1) -> null_a__U41 [0] a__U51(v0, v1, v2) -> null_a__U51 [0] a__U52(v0, v1, v2) -> null_a__U52 [0] a__U61(v0) -> null_a__U61 [0] a__U71(v0, v1, v2) -> null_a__U71 [0] a__U72(v0, v1, v2) -> null_a__U72 [0] a__isNat(v0) -> null_a__isNat [0] a__plus(v0, v1) -> null_a__plus [0] a__x(v0, v1) -> null_a__x [0] mark(v0) -> null_mark [0] A__U41(v0, v1) -> null_A__U41 [0] A__U51(v0, v1, v2) -> null_A__U51 [0] A__U52(v0, v1, v2) -> null_A__U52 [0] A__U71(v0, v1, v2) -> null_A__U71 [0] A__U72(v0, v1, v2) -> null_A__U72 [0] A__ISNAT(v0) -> null_A__ISNAT [0] A__PLUS(v0, v1) -> null_A__PLUS [0] A__X(v0, v1) -> null_A__X [0] MARK(v0) -> null_MARK [0] A__U11(v0, v1) -> null_A__U11 [0] A__U31(v0, v1) -> null_A__U31 [0] The TRS has the following type information: A__U41 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> c10:null_A__U41 tt :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark c10 :: c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47:null_MARK -> c10:null_A__U41 MARK :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47:null_MARK A__U51 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> c12:null_A__U51 c12 :: c14:c15:null_A__U52 -> c26:c28:c27:null_A__ISNAT -> c12:null_A__U51 A__U52 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> c14:c15:null_A__U52 a__isNat :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark A__ISNAT :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> c26:c28:c27:null_A__ISNAT c14 :: c30:c31:null_A__PLUS -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47:null_MARK -> c14:c15:null_A__U52 A__PLUS :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> c30:c31:null_A__PLUS mark :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark c15 :: c30:c31:null_A__PLUS -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47:null_MARK -> c14:c15:null_A__U52 A__U71 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> c19:null_A__U71 c19 :: c21:c22:c23:null_A__U72 -> c26:c28:c27:null_A__ISNAT -> c19:null_A__U71 A__U72 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> c21:c22:c23:null_A__U72 c21 :: c30:c31:null_A__PLUS -> c34:c33:null_A__X -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47:null_MARK -> c21:c22:c23:null_A__U72 a__x :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark A__X :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> c34:c33:null_A__X c22 :: c30:c31:null_A__PLUS -> c34:c33:null_A__X -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47:null_MARK -> c21:c22:c23:null_A__U72 c23 :: c30:c31:null_A__PLUS -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47:null_MARK -> c21:c22:c23:null_A__U72 plus :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark c26 :: c:null_A__U11 -> c26:c28:c27:null_A__ISNAT -> c26:c28:c27:null_A__ISNAT A__U11 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> c:null_A__U11 x :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark c28 :: c6:null_A__U31 -> c26:c28:c27:null_A__ISNAT -> c26:c28:c27:null_A__ISNAT A__U31 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> c6:null_A__U31 0 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark c30 :: c10:null_A__U41 -> c26:c28:c27:null_A__ISNAT -> c30:c31:null_A__PLUS s :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark c31 :: c12:null_A__U51 -> c26:c28:c27:null_A__ISNAT -> c30:c31:null_A__PLUS c34 :: c19:null_A__U71 -> c26:c28:c27:null_A__ISNAT -> c34:c33:null_A__X U11 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark c36 :: c:null_A__U11 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47:null_MARK -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47:null_MARK isNat :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark c38 :: c26:c28:c27:null_A__ISNAT -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47:null_MARK U31 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark c40 :: c6:null_A__U31 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47:null_MARK -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47:null_MARK U41 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark c42 :: c10:null_A__U41 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47:null_MARK -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47:null_MARK U51 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark c43 :: c12:null_A__U51 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47:null_MARK -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47:null_MARK U52 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark c44 :: c14:c15:null_A__U52 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47:null_MARK -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47:null_MARK c45 :: c30:c31:null_A__PLUS -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47:null_MARK -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47:null_MARK c46 :: c30:c31:null_A__PLUS -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47:null_MARK -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47:null_MARK U71 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark c48 :: c19:null_A__U71 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47:null_MARK -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47:null_MARK U72 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark c49 :: c21:c22:c23:null_A__U72 -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47:null_MARK -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47:null_MARK c50 :: c34:c33:null_A__X -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47:null_MARK -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47:null_MARK c51 :: c34:c33:null_A__X -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47:null_MARK -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47:null_MARK c53 :: c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47:null_MARK -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47:null_MARK c :: c26:c28:c27:null_A__ISNAT -> c:null_A__U11 c6 :: c26:c28:c27:null_A__ISNAT -> c6:null_A__U31 c27 :: c26:c28:c27:null_A__ISNAT -> c26:c28:c27:null_A__ISNAT c33 :: c26:c28:c27:null_A__ISNAT -> c34:c33:null_A__X U12 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark c37 :: c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47:null_MARK -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47:null_MARK U21 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark c39 :: c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47:null_MARK -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47:null_MARK U32 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark c41 :: c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47:null_MARK -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47:null_MARK U61 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark c47 :: c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47:null_MARK -> c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47:null_MARK a__U11 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> 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tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark a__U31 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark a__U32 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark a__U41 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark a__U51 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark a__U52 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark a__plus :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark a__U61 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark a__U71 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark -> 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tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark null_a__U21 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark null_a__U31 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark null_a__U32 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark null_a__U41 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark null_a__U51 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark null_a__U52 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark null_a__U61 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark null_a__U71 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark null_a__U72 :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark null_a__isNat :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark null_a__plus :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark null_a__x :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark null_mark :: tt:plus:x:0:s:U11:isNat:U31:U41:U51:U52:U71:U72:U12:U21:U32:U61:null_a__U11:null_a__U12:null_a__U21:null_a__U31:null_a__U32:null_a__U41:null_a__U51:null_a__U52:null_a__U61:null_a__U71:null_a__U72:null_a__isNat:null_a__plus:null_a__x:null_mark null_A__U41 :: c10:null_A__U41 null_A__U51 :: c12:null_A__U51 null_A__U52 :: c14:c15:null_A__U52 null_A__U71 :: c19:null_A__U71 null_A__U72 :: c21:c22:c23:null_A__U72 null_A__ISNAT :: c26:c28:c27:null_A__ISNAT null_A__PLUS :: c30:c31:null_A__PLUS null_A__X :: c34:c33:null_A__X null_MARK :: c36:c38:c40:c42:c43:c44:c45:c46:c48:c49:c50:c51:c53:c37:c39:c41:c47:null_MARK null_A__U11 :: c:null_A__U11 null_A__U31 :: c6:null_A__U31 Rewrite Strategy: INNERMOST ---------------------------------------- (55) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: tt => 1 0 => 0 null_a__U11 => 0 null_a__U12 => 0 null_a__U21 => 0 null_a__U31 => 0 null_a__U32 => 0 null_a__U41 => 0 null_a__U51 => 0 null_a__U52 => 0 null_a__U61 => 0 null_a__U71 => 0 null_a__U72 => 0 null_a__isNat => 0 null_a__plus => 0 null_a__x => 0 null_mark => 0 null_A__U41 => 0 null_A__U51 => 0 null_A__U52 => 0 null_A__U71 => 0 null_A__U72 => 0 null_A__ISNAT => 0 null_A__PLUS => 0 null_A__X => 0 null_MARK => 0 null_A__U11 => 0 null_A__U31 => 0 ---------------------------------------- (56) Obligation: Complexity RNTS consisting of the following rules: A__ISNAT(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 A__ISNAT(z) -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1 + z0, z0 >= 0 A__ISNAT(z) -{ 1 }-> 1 + A__U31(a__isNat(z0), z1) + A__ISNAT(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__ISNAT(z) -{ 1 }-> 1 + A__U11(a__isNat(z0), z1) + A__ISNAT(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 A__PLUS(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__PLUS(z, z') -{ 1 }-> 1 + A__U51(a__isNat(z1), z1, z0) + A__ISNAT(z1) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 A__PLUS(z, z') -{ 1 }-> 1 + A__U41(a__isNat(z0), z0) + A__ISNAT(z0) :|: z = z0, z0 >= 0, z' = 0 A__U11(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__U11(z, z') -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1, z0 >= 0, z' = z0 A__U31(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__U31(z, z') -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1, z0 >= 0, z' = z0 A__U41(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__U41(z, z') -{ 1 }-> 1 + MARK(z0) :|: z = 1, z0 >= 0, z' = z0 A__U51(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 A__U51(z, z', z'') -{ 1 }-> 1 + A__U52(a__isNat(z1), z0, z1) + A__ISNAT(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U52(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 A__U52(z, z', z'') -{ 1 }-> 1 + A__PLUS(mark(z1), mark(z0)) + MARK(z0) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U52(z, z', z'') -{ 1 }-> 1 + A__PLUS(mark(z1), mark(z0)) + MARK(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U71(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 A__U71(z, z', z'') -{ 1 }-> 1 + A__U72(a__isNat(z1), z0, z1) + A__ISNAT(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U72(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 A__U72(z, z', z'') -{ 1 }-> 1 + A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)) + MARK(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U72(z, z', z'') -{ 1 }-> 1 + A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)) + A__X(mark(z1), mark(z0)) + MARK(z0) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__U72(z, z', z'') -{ 1 }-> 1 + A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)) + A__X(mark(z1), mark(z0)) + MARK(z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 A__X(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 A__X(z, z') -{ 1 }-> 1 + A__ISNAT(z0) :|: z = z0, z0 >= 0, z' = 0 A__X(z, z') -{ 1 }-> 1 + A__U71(a__isNat(z1), z1, z0) + A__ISNAT(z1) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 MARK(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 MARK(z) -{ 1 }-> 1 + MARK(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__ISNAT(z0) :|: z = 1 + z0, z0 >= 0 MARK(z) -{ 1 }-> 1 + A__X(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__X(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U72(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U71(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U52(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U51(mark(z0), z1, z2) + MARK(z0) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 MARK(z) -{ 1 }-> 1 + A__U41(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U31(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__U11(mark(z0), z1) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z0) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 MARK(z) -{ 1 }-> 1 + A__PLUS(mark(z0), mark(z1)) + MARK(z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__U11(z, z') -{ 0 }-> a__U12(a__isNat(z0)) :|: z = 1, z0 >= 0, z' = z0 a__U11(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U11(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U12(z) -{ 0 }-> 1 :|: z = 1 a__U12(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U12(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U21(z) -{ 0 }-> 1 :|: z = 1 a__U21(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U21(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U31(z, z') -{ 0 }-> a__U32(a__isNat(z0)) :|: z = 1, z0 >= 0, z' = z0 a__U31(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U31(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U32(z) -{ 0 }-> 1 :|: z = 1 a__U32(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U32(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U41(z, z') -{ 0 }-> mark(z0) :|: z = 1, z0 >= 0, z' = z0 a__U41(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__U41(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__U51(z, z', z'') -{ 0 }-> a__U52(a__isNat(z1), z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U51(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U51(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__U52(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U52(z, z', z'') -{ 0 }-> 1 + a__plus(mark(z1), mark(z0)) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U52(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__U61(z) -{ 0 }-> 0 :|: z = 1 a__U61(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__U61(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__U71(z, z', z'') -{ 0 }-> a__U72(a__isNat(z1), z0, z1) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U71(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U71(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__U72(z, z', z'') -{ 0 }-> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) :|: z1 >= 0, z = 1, z0 >= 0, z' = z0, z'' = z1 a__U72(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 a__U72(z, z', z'') -{ 0 }-> 1 + z0 + z1 + z2 :|: z'' = z2, z = z0, z1 >= 0, z' = z1, z0 >= 0, z2 >= 0 a__isNat(z) -{ 0 }-> a__U31(a__isNat(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNat(z) -{ 0 }-> a__U21(a__isNat(z0)) :|: z = 1 + z0, z0 >= 0 a__isNat(z) -{ 0 }-> a__U11(a__isNat(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 a__isNat(z) -{ 0 }-> 1 :|: z = 0 a__isNat(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 a__isNat(z) -{ 0 }-> 1 + z0 :|: z = z0, z0 >= 0 a__plus(z, z') -{ 0 }-> a__U51(a__isNat(z1), z1, z0) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 a__plus(z, z') -{ 0 }-> a__U41(a__isNat(z0), z0) :|: z = z0, z0 >= 0, z' = 0 a__plus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__plus(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 a__x(z, z') -{ 0 }-> a__U71(a__isNat(z1), z1, z0) :|: z = z0, z1 >= 0, z0 >= 0, z' = 1 + z1 a__x(z, z') -{ 0 }-> a__U61(a__isNat(z0)) :|: z = z0, z0 >= 0, z' = 0 a__x(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 a__x(z, z') -{ 0 }-> 1 + z0 + z1 :|: z = z0, z1 >= 0, z' = z1, z0 >= 0 mark(z) -{ 0 }-> a__x(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__plus(mark(z0), mark(z1)) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__isNat(z0) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U72(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U71(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U61(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U52(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U51(mark(z0), z1, z2) :|: z1 >= 0, z = 1 + z0 + z1 + z2, z0 >= 0, z2 >= 0 mark(z) -{ 0 }-> a__U41(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U32(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U31(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> a__U21(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U12(mark(z0)) :|: z = 1 + z0, z0 >= 0 mark(z) -{ 0 }-> a__U11(mark(z0), z1) :|: z1 >= 0, z0 >= 0, z = 1 + z0 + z1 mark(z) -{ 0 }-> 1 :|: z = 1 mark(z) -{ 0 }-> 0 :|: z = 0 mark(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 mark(z) -{ 0 }-> 1 + mark(z0) :|: z = 1 + z0, z0 >= 0 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (57) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U51(tt, z0, z1) -> c12(A__U52(a__isNat(z1), z0, z1), A__ISNAT(z1)) by A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0), A__ISNAT(0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, z0) -> c12(A__U52(isNat(z0), x0, z0), A__ISNAT(z0)) ---------------------------------------- (58) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__U52(tt, z0, z1) -> c14(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U52(tt, z0, z1) -> c15(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U71(tt, z0, z1) -> c19(A__U72(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U72(tt, z0, z1) -> c21(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) A__U72(tt, z0, z1) -> c22(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0), A__ISNAT(0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, z0) -> c12(A__U52(isNat(z0), x0, z0), A__ISNAT(z0)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__U52(tt, z0, z1) -> c14(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U52(tt, z0, z1) -> c15(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U71(tt, z0, z1) -> c19(A__U72(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U72(tt, z0, z1) -> c21(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) A__U72(tt, z0, z1) -> c22(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0), A__ISNAT(0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, z0) -> c12(A__U52(isNat(z0), x0, z0), A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, A__U52_3, A__U71_3, A__U72_3, A__ISNAT_1, A__PLUS_2, A__X_2, MARK_1, A__U11_2, A__U31_2, A__U51_3 Compound Symbols: c10_1, c14_2, c15_2, c19_2, c21_3, c22_3, c23_2, c26_2, c28_2, c30_2, c31_2, c34_2, c36_2, c38_1, c40_2, c42_2, c43_2, c44_2, c45_2, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2 ---------------------------------------- (59) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (60) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__U52(tt, z0, z1) -> c14(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U52(tt, z0, z1) -> c15(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U71(tt, z0, z1) -> c19(A__U72(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U72(tt, z0, z1) -> c21(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) A__U72(tt, z0, z1) -> c22(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__U52(tt, z0, z1) -> c14(A__PLUS(mark(z1), mark(z0)), MARK(z1)) A__U52(tt, z0, z1) -> c15(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U71(tt, z0, z1) -> c19(A__U72(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U72(tt, z0, z1) -> c21(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) A__U72(tt, z0, z1) -> c22(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, A__U52_3, A__U71_3, A__U72_3, A__ISNAT_1, A__PLUS_2, A__X_2, MARK_1, A__U11_2, A__U31_2, A__U51_3 Compound Symbols: c10_1, c14_2, c15_2, c19_2, c21_3, c22_3, c23_2, c26_2, c28_2, c30_2, c31_2, c34_2, c36_2, c38_1, c40_2, c42_2, c43_2, c44_2, c45_2, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1 ---------------------------------------- (61) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U52(tt, z0, z1) -> c14(A__PLUS(mark(z1), mark(z0)), MARK(z1)) by A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, tt, x1) -> c14(A__PLUS(mark(x1), tt), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0)), MARK(tt)) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0)), MARK(0)) ---------------------------------------- (62) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__U52(tt, z0, z1) -> c15(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U71(tt, z0, z1) -> c19(A__U72(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U72(tt, z0, z1) -> c21(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) A__U72(tt, z0, z1) -> c22(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, tt, x1) -> c14(A__PLUS(mark(x1), tt), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0)), MARK(tt)) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0)), MARK(0)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__U52(tt, z0, z1) -> c15(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U71(tt, z0, z1) -> c19(A__U72(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U72(tt, z0, z1) -> c21(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) A__U72(tt, z0, z1) -> c22(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, tt, x1) -> c14(A__PLUS(mark(x1), tt), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0)), MARK(tt)) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, A__U52_3, A__U71_3, A__U72_3, A__ISNAT_1, A__PLUS_2, A__X_2, MARK_1, A__U11_2, A__U31_2, A__U51_3 Compound Symbols: c10_1, c15_2, c19_2, c21_3, c22_3, c23_2, c26_2, c28_2, c30_2, c31_2, c34_2, c36_2, c38_1, c40_2, c42_2, c43_2, c44_2, c45_2, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2 ---------------------------------------- (63) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (64) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__U52(tt, z0, z1) -> c15(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U71(tt, z0, z1) -> c19(A__U72(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U72(tt, z0, z1) -> c21(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) A__U72(tt, z0, z1) -> c22(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__U52(tt, z0, z1) -> c15(A__PLUS(mark(z1), mark(z0)), MARK(z0)) A__U71(tt, z0, z1) -> c19(A__U72(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U72(tt, z0, z1) -> c21(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) A__U72(tt, z0, z1) -> c22(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, A__U52_3, A__U71_3, A__U72_3, A__ISNAT_1, A__PLUS_2, A__X_2, MARK_1, A__U11_2, A__U31_2, A__U51_3 Compound Symbols: c10_1, c15_2, c19_2, c21_3, c22_3, c23_2, c26_2, c28_2, c30_2, c31_2, c34_2, c36_2, c38_1, c40_2, c42_2, c43_2, c44_2, c45_2, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1 ---------------------------------------- (65) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U52(tt, z0, z1) -> c15(A__PLUS(mark(z1), mark(z0)), MARK(z0)) by A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, tt, x1) -> c15(A__PLUS(mark(x1), tt), MARK(tt)) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0), MARK(0)) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) ---------------------------------------- (66) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__U71(tt, z0, z1) -> c19(A__U72(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U72(tt, z0, z1) -> c21(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) A__U72(tt, z0, z1) -> c22(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, tt, x1) -> c15(A__PLUS(mark(x1), tt), MARK(tt)) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0), MARK(0)) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__U71(tt, z0, z1) -> c19(A__U72(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U72(tt, z0, z1) -> c21(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) A__U72(tt, z0, z1) -> c22(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, tt, x1) -> c15(A__PLUS(mark(x1), tt), MARK(tt)) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0), MARK(0)) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, A__U71_3, A__U72_3, A__ISNAT_1, A__PLUS_2, A__X_2, MARK_1, A__U11_2, A__U31_2, A__U51_3, A__U52_3 Compound Symbols: c10_1, c19_2, c21_3, c22_3, c23_2, c26_2, c28_2, c30_2, c31_2, c34_2, c36_2, c38_1, c40_2, c42_2, c43_2, c44_2, c45_2, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2 ---------------------------------------- (67) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U52(tt, tt, x1) -> c15(A__PLUS(mark(x1), tt), MARK(tt)) ---------------------------------------- (68) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__U71(tt, z0, z1) -> c19(A__U72(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U72(tt, z0, z1) -> c21(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) A__U72(tt, z0, z1) -> c22(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0), MARK(0)) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__U71(tt, z0, z1) -> c19(A__U72(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U72(tt, z0, z1) -> c21(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) A__U72(tt, z0, z1) -> c22(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0), MARK(0)) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, A__U71_3, A__U72_3, A__ISNAT_1, A__PLUS_2, A__X_2, MARK_1, A__U11_2, A__U31_2, A__U51_3, A__U52_3 Compound Symbols: c10_1, c19_2, c21_3, c22_3, c23_2, c26_2, c28_2, c30_2, c31_2, c34_2, c36_2, c38_1, c40_2, c42_2, c43_2, c44_2, c45_2, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2 ---------------------------------------- (69) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (70) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__U71(tt, z0, z1) -> c19(A__U72(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U72(tt, z0, z1) -> c21(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) A__U72(tt, z0, z1) -> c22(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__U71(tt, z0, z1) -> c19(A__U72(a__isNat(z1), z0, z1), A__ISNAT(z1)) A__U72(tt, z0, z1) -> c21(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) A__U72(tt, z0, z1) -> c22(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, A__U71_3, A__U72_3, A__ISNAT_1, A__PLUS_2, A__X_2, MARK_1, A__U11_2, A__U31_2, A__U51_3, A__U52_3 Compound Symbols: c10_1, c19_2, c21_3, c22_3, c23_2, c26_2, c28_2, c30_2, c31_2, c34_2, c36_2, c38_1, c40_2, c42_2, c43_2, c44_2, c45_2, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1 ---------------------------------------- (71) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U71(tt, z0, z1) -> c19(A__U72(a__isNat(z1), z0, z1), A__ISNAT(z1)) by A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0), A__ISNAT(0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, z0) -> c19(A__U72(isNat(z0), x0, z0), A__ISNAT(z0)) ---------------------------------------- (72) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__U72(tt, z0, z1) -> c21(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) A__U72(tt, z0, z1) -> c22(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0), A__ISNAT(0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, z0) -> c19(A__U72(isNat(z0), x0, z0), A__ISNAT(z0)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__U72(tt, z0, z1) -> c21(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) A__U72(tt, z0, z1) -> c22(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0), A__ISNAT(0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, z0) -> c19(A__U72(isNat(z0), x0, z0), A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, A__U72_3, A__ISNAT_1, A__PLUS_2, A__X_2, MARK_1, A__U11_2, A__U31_2, A__U51_3, A__U52_3, A__U71_3 Compound Symbols: c10_1, c21_3, c22_3, c23_2, c26_2, c28_2, c30_2, c31_2, c34_2, c36_2, c38_1, c40_2, c42_2, c43_2, c44_2, c45_2, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2 ---------------------------------------- (73) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (74) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__U72(tt, z0, z1) -> c21(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) A__U72(tt, z0, z1) -> c22(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__U72(tt, z0, z1) -> c21(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) A__U72(tt, z0, z1) -> c22(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, A__U72_3, A__ISNAT_1, A__PLUS_2, A__X_2, MARK_1, A__U11_2, A__U31_2, A__U51_3, A__U52_3, A__U71_3 Compound Symbols: c10_1, c21_3, c22_3, c23_2, c26_2, c28_2, c30_2, c31_2, c34_2, c36_2, c38_1, c40_2, c42_2, c43_2, c44_2, c45_2, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1 ---------------------------------------- (75) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U72(tt, z0, z1) -> c21(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z1)) by A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(mark(tt), mark(x0)), tt), A__X(mark(tt), mark(x0)), MARK(tt)) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(0)) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(tt)) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(0)) ---------------------------------------- (76) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__U72(tt, z0, z1) -> c22(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(mark(tt), mark(x0)), tt), A__X(mark(tt), mark(x0)), MARK(tt)) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(0)) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(tt)) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(0)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__U72(tt, z0, z1) -> c22(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(mark(tt), mark(x0)), tt), A__X(mark(tt), mark(x0)), MARK(tt)) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(0)) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(tt)) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, A__U72_3, A__ISNAT_1, A__PLUS_2, A__X_2, MARK_1, A__U11_2, A__U31_2, A__U51_3, A__U52_3, A__U71_3 Compound Symbols: c10_1, c22_3, c23_2, c26_2, c28_2, c30_2, c31_2, c34_2, c36_2, c38_1, c40_2, c42_2, c43_2, c44_2, c45_2, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3 ---------------------------------------- (77) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 5 trailing tuple parts ---------------------------------------- (78) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__U72(tt, z0, z1) -> c22(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__U72(tt, z0, z1) -> c22(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, A__U72_3, A__ISNAT_1, A__PLUS_2, A__X_2, MARK_1, A__U11_2, A__U31_2, A__U51_3, A__U52_3, A__U71_3 Compound Symbols: c10_1, c22_3, c23_2, c26_2, c28_2, c30_2, c31_2, c34_2, c36_2, c38_1, c40_2, c42_2, c43_2, c44_2, c45_2, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2 ---------------------------------------- (79) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U72(tt, z0, z1) -> c22(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), A__X(mark(z1), mark(z0)), MARK(z0)) by A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(mark(tt), mark(x0)), tt), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(tt)) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(0)) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) ---------------------------------------- (80) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(mark(tt), mark(x0)), tt), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(tt)) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(0)) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(mark(tt), mark(x0)), tt), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(tt)) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(0)) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, A__U72_3, A__ISNAT_1, A__PLUS_2, A__X_2, MARK_1, A__U11_2, A__U31_2, A__U51_3, A__U52_3, A__U71_3 Compound Symbols: c10_1, c23_2, c26_2, c28_2, c30_2, c31_2, c34_2, c36_2, c38_1, c40_2, c42_2, c43_2, c44_2, c45_2, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3 ---------------------------------------- (81) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (82) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, A__U72_3, A__ISNAT_1, A__PLUS_2, A__X_2, MARK_1, A__U11_2, A__U31_2, A__U51_3, A__U52_3, A__U71_3 Compound Symbols: c10_1, c23_2, c26_2, c28_2, c30_2, c31_2, c34_2, c36_2, c38_1, c40_2, c42_2, c43_2, c44_2, c45_2, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2 ---------------------------------------- (83) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U72(tt, z0, z1) -> c23(A__PLUS(a__x(mark(z1), mark(z0)), mark(z1)), MARK(z1)) by A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(mark(tt), mark(x0)), tt), MARK(tt)) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0), MARK(0)) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt)), MARK(tt)) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0)), MARK(0)) ---------------------------------------- (84) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(mark(tt), mark(x0)), tt), MARK(tt)) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0), MARK(0)) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt)), MARK(tt)) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0)), MARK(0)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(mark(tt), mark(x0)), tt), MARK(tt)) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0), MARK(0)) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt)), MARK(tt)) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, A__ISNAT_1, A__PLUS_2, A__X_2, MARK_1, A__U11_2, A__U31_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3 Compound Symbols: c10_1, c26_2, c28_2, c30_2, c31_2, c34_2, c36_2, c38_1, c40_2, c42_2, c43_2, c44_2, c45_2, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2 ---------------------------------------- (85) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(mark(tt), mark(x0)), tt), MARK(tt)) ---------------------------------------- (86) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0), MARK(0)) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt)), MARK(tt)) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0)), MARK(0)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0), MARK(0)) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt)), MARK(tt)) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, A__ISNAT_1, A__PLUS_2, A__X_2, MARK_1, A__U11_2, A__U31_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3 Compound Symbols: c10_1, c26_2, c28_2, c30_2, c31_2, c34_2, c36_2, c38_1, c40_2, c42_2, c43_2, c44_2, c45_2, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2 ---------------------------------------- (87) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (88) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, A__ISNAT_1, A__PLUS_2, A__X_2, MARK_1, A__U11_2, A__U31_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3 Compound Symbols: c10_1, c26_2, c28_2, c30_2, c31_2, c34_2, c36_2, c38_1, c40_2, c42_2, c43_2, c44_2, c45_2, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1 ---------------------------------------- (89) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ISNAT(plus(z0, z1)) -> c26(A__U11(a__isNat(z0), z1), A__ISNAT(z0)) by A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1), A__ISNAT(0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(z0, x1)) -> c26(A__U11(isNat(z0), x1), A__ISNAT(z0)) ---------------------------------------- (90) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1), A__ISNAT(0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(z0, x1)) -> c26(A__U11(isNat(z0), x1), A__ISNAT(z0)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1), A__ISNAT(0)) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(z0, x1)) -> c26(A__U11(isNat(z0), x1), A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, A__ISNAT_1, A__PLUS_2, A__X_2, MARK_1, A__U11_2, A__U31_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3 Compound Symbols: c10_1, c28_2, c30_2, c31_2, c34_2, c36_2, c38_1, c40_2, c42_2, c43_2, c44_2, c45_2, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2 ---------------------------------------- (91) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (92) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, A__ISNAT_1, A__PLUS_2, A__X_2, MARK_1, A__U11_2, A__U31_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3 Compound Symbols: c10_1, c28_2, c30_2, c31_2, c34_2, c36_2, c38_1, c40_2, c42_2, c43_2, c44_2, c45_2, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1 ---------------------------------------- (93) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__ISNAT(x(z0, z1)) -> c28(A__U31(a__isNat(z0), z1), A__ISNAT(z0)) by A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1), A__ISNAT(0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(z0, x1)) -> c28(A__U31(isNat(z0), x1), A__ISNAT(z0)) ---------------------------------------- (94) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1), A__ISNAT(0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(z0, x1)) -> c28(A__U31(isNat(z0), x1), A__ISNAT(z0)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1), A__ISNAT(0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(z0, x1)) -> c28(A__U31(isNat(z0), x1), A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, A__PLUS_2, A__X_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__U51_3, A__U52_3, A__U71_3, A__U72_3 Compound Symbols: c10_1, c30_2, c31_2, c34_2, c36_2, c38_1, c40_2, c42_2, c43_2, c44_2, c45_2, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2 ---------------------------------------- (95) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (96) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, A__PLUS_2, A__X_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__U51_3, A__U52_3, A__U71_3, A__U72_3 Compound Symbols: c10_1, c30_2, c31_2, c34_2, c36_2, c38_1, c40_2, c42_2, c43_2, c44_2, c45_2, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1 ---------------------------------------- (97) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(z0, 0) -> c30(A__U41(a__isNat(z0), z0), A__ISNAT(z0)) by A__PLUS(0, 0) -> c30(A__U41(tt, 0), A__ISNAT(0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(z0, 0) -> c30(A__U41(isNat(z0), z0), A__ISNAT(z0)) ---------------------------------------- (98) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(0, 0) -> c30(A__U41(tt, 0), A__ISNAT(0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(z0, 0) -> c30(A__U41(isNat(z0), z0), A__ISNAT(z0)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(0, 0) -> c30(A__U41(tt, 0), A__ISNAT(0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(z0, 0) -> c30(A__U41(isNat(z0), z0), A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, A__PLUS_2, A__X_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__U51_3, A__U52_3, A__U71_3, A__U72_3 Compound Symbols: c10_1, c31_2, c34_2, c36_2, c38_1, c40_2, c42_2, c43_2, c44_2, c45_2, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2 ---------------------------------------- (99) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (100) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, A__PLUS_2, A__X_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__U51_3, A__U52_3, A__U71_3, A__U72_3 Compound Symbols: c10_1, c31_2, c34_2, c36_2, c38_1, c40_2, c42_2, c43_2, c44_2, c45_2, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1 ---------------------------------------- (101) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__PLUS(z0, s(z1)) -> c31(A__U51(a__isNat(z1), z1, z0), A__ISNAT(z1)) by A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0), A__ISNAT(0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(z0)) -> c31(A__U51(isNat(z0), z0, x0), A__ISNAT(z0)) ---------------------------------------- (102) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0), A__ISNAT(0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(z0)) -> c31(A__U51(isNat(z0), z0, x0), A__ISNAT(z0)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0), A__ISNAT(0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(z0)) -> c31(A__U51(isNat(z0), z0, x0), A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, A__X_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c34_2, c36_2, c38_1, c40_2, c42_2, c43_2, c44_2, c45_2, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2 ---------------------------------------- (103) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (104) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, A__X_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c34_2, c36_2, c38_1, c40_2, c42_2, c43_2, c44_2, c45_2, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1 ---------------------------------------- (105) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__X(z0, s(z1)) -> c34(A__U71(a__isNat(z1), z1, z0), A__ISNAT(z1)) by A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0), A__ISNAT(0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(z0)) -> c34(A__U71(isNat(z0), z0, x0), A__ISNAT(z0)) ---------------------------------------- (106) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0), A__ISNAT(0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(z0)) -> c34(A__U71(isNat(z0), z0, x0), A__ISNAT(z0)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0), A__ISNAT(0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(z0)) -> c34(A__U71(isNat(z0), z0, x0), A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c36_2, c38_1, c40_2, c42_2, c43_2, c44_2, c45_2, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2 ---------------------------------------- (107) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (108) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c36_2, c38_1, c40_2, c42_2, c43_2, c44_2, c45_2, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1 ---------------------------------------- (109) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U11(z0, z1)) -> c36(A__U11(mark(z0), z1), MARK(z0)) by MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c36(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1), MARK(tt)) MARK(U11(s(z0), x1)) -> c36(A__U11(s(mark(z0)), x1), MARK(s(z0))) MARK(U11(0, x1)) -> c36(A__U11(0, x1), MARK(0)) ---------------------------------------- (110) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c36(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1), MARK(tt)) MARK(U11(s(z0), x1)) -> c36(A__U11(s(mark(z0)), x1), MARK(s(z0))) MARK(U11(0, x1)) -> c36(A__U11(0, x1), MARK(0)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c36(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1), MARK(tt)) MARK(U11(s(z0), x1)) -> c36(A__U11(s(mark(z0)), x1), MARK(s(z0))) MARK(U11(0, x1)) -> c36(A__U11(0, x1), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c40_2, c42_2, c43_2, c44_2, c45_2, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2 ---------------------------------------- (111) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U11(0, x1)) -> c36(A__U11(0, x1), MARK(0)) ---------------------------------------- (112) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c36(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1), MARK(tt)) MARK(U11(s(z0), x1)) -> c36(A__U11(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c36(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1), MARK(tt)) MARK(U11(s(z0), x1)) -> c36(A__U11(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c40_2, c42_2, c43_2, c44_2, c45_2, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2 ---------------------------------------- (113) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (114) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c36(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(isNat(z0), x1)) -> c36(A__U11(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c40_2, c42_2, c43_2, c44_2, c45_2, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1 ---------------------------------------- (115) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (116) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c40_2, c42_2, c43_2, c44_2, c45_2, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1 ---------------------------------------- (117) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U31(z0, z1)) -> c40(A__U31(mark(z0), z1), MARK(z0)) by MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c40(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1), MARK(tt)) MARK(U31(s(z0), x1)) -> c40(A__U31(s(mark(z0)), x1), MARK(s(z0))) MARK(U31(0, x1)) -> c40(A__U31(0, x1), MARK(0)) ---------------------------------------- (118) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c40(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1), MARK(tt)) MARK(U31(s(z0), x1)) -> c40(A__U31(s(mark(z0)), x1), MARK(s(z0))) MARK(U31(0, x1)) -> c40(A__U31(0, x1), MARK(0)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c40(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1), MARK(tt)) MARK(U31(s(z0), x1)) -> c40(A__U31(s(mark(z0)), x1), MARK(s(z0))) MARK(U31(0, x1)) -> c40(A__U31(0, x1), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c42_2, c43_2, c44_2, c45_2, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2 ---------------------------------------- (119) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U31(0, x1)) -> c40(A__U31(0, x1), MARK(0)) ---------------------------------------- (120) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c40(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1), MARK(tt)) MARK(U31(s(z0), x1)) -> c40(A__U31(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c40(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1), MARK(tt)) MARK(U31(s(z0), x1)) -> c40(A__U31(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c42_2, c43_2, c44_2, c45_2, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2 ---------------------------------------- (121) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (122) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c40(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(isNat(z0), x1)) -> c40(A__U31(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c42_2, c43_2, c44_2, c45_2, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1 ---------------------------------------- (123) CdtGraphSplitRhsProof (BOTH BOUNDS(ID, ID)) Split RHS of tuples not part of any SCC ---------------------------------------- (124) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c42_2, c43_2, c44_2, c45_2, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1 ---------------------------------------- (125) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U41(z0, z1)) -> c42(A__U41(mark(z0), z1), MARK(z0)) by MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1), MARK(tt)) MARK(U41(s(z0), x1)) -> c42(A__U41(s(mark(z0)), x1), MARK(s(z0))) MARK(U41(0, x1)) -> c42(A__U41(0, x1), MARK(0)) ---------------------------------------- (126) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1), MARK(tt)) MARK(U41(s(z0), x1)) -> c42(A__U41(s(mark(z0)), x1), MARK(s(z0))) MARK(U41(0, x1)) -> c42(A__U41(0, x1), MARK(0)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1), MARK(tt)) MARK(U41(s(z0), x1)) -> c42(A__U41(s(mark(z0)), x1), MARK(s(z0))) MARK(U41(0, x1)) -> c42(A__U41(0, x1), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c43_2, c44_2, c45_2, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2 ---------------------------------------- (127) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U41(0, x1)) -> c42(A__U41(0, x1), MARK(0)) ---------------------------------------- (128) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1), MARK(tt)) MARK(U41(s(z0), x1)) -> c42(A__U41(s(mark(z0)), x1), MARK(s(z0))) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1), MARK(tt)) MARK(U41(s(z0), x1)) -> c42(A__U41(s(mark(z0)), x1), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c43_2, c44_2, c45_2, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2 ---------------------------------------- (129) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (130) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c43_2, c44_2, c45_2, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1 ---------------------------------------- (131) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U51(z0, z1, z2)) -> c43(A__U51(mark(z0), z1, z2), MARK(z0)) by MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2), MARK(tt)) MARK(U51(s(z0), x1, x2)) -> c43(A__U51(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U51(0, x1, x2)) -> c43(A__U51(0, x1, x2), MARK(0)) ---------------------------------------- (132) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2), MARK(tt)) MARK(U51(s(z0), x1, x2)) -> c43(A__U51(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U51(0, x1, x2)) -> c43(A__U51(0, x1, x2), MARK(0)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2), MARK(tt)) MARK(U51(s(z0), x1, x2)) -> c43(A__U51(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U51(0, x1, x2)) -> c43(A__U51(0, x1, x2), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c44_2, c45_2, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2 ---------------------------------------- (133) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U51(0, x1, x2)) -> c43(A__U51(0, x1, x2), MARK(0)) ---------------------------------------- (134) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2), MARK(tt)) MARK(U51(s(z0), x1, x2)) -> c43(A__U51(s(mark(z0)), x1, x2), MARK(s(z0))) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2), MARK(tt)) MARK(U51(s(z0), x1, x2)) -> c43(A__U51(s(mark(z0)), x1, x2), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c44_2, c45_2, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2 ---------------------------------------- (135) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (136) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c44_2, c45_2, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2, c43_1 ---------------------------------------- (137) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U52(z0, z1, z2)) -> c44(A__U52(mark(z0), z1, z2), MARK(z0)) by MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2), MARK(tt)) MARK(U52(s(z0), x1, x2)) -> c44(A__U52(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U52(0, x1, x2)) -> c44(A__U52(0, x1, x2), MARK(0)) ---------------------------------------- (138) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2), MARK(tt)) MARK(U52(s(z0), x1, x2)) -> c44(A__U52(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U52(0, x1, x2)) -> c44(A__U52(0, x1, x2), MARK(0)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2), MARK(tt)) MARK(U52(s(z0), x1, x2)) -> c44(A__U52(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U52(0, x1, x2)) -> c44(A__U52(0, x1, x2), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c45_2, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2, c43_1, c44_2 ---------------------------------------- (139) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U52(0, x1, x2)) -> c44(A__U52(0, x1, x2), MARK(0)) ---------------------------------------- (140) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2), MARK(tt)) MARK(U52(s(z0), x1, x2)) -> c44(A__U52(s(mark(z0)), x1, x2), MARK(s(z0))) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2), MARK(tt)) MARK(U52(s(z0), x1, x2)) -> c44(A__U52(s(mark(z0)), x1, x2), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c45_2, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2, c43_1, c44_2 ---------------------------------------- (141) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (142) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c45_2, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2, c43_1, c44_2, c44_1 ---------------------------------------- (143) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(z0, z1)) -> c45(A__PLUS(mark(z0), mark(z1)), MARK(z0)) by MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, tt)) -> c45(A__PLUS(mark(x0), tt), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1)), MARK(tt)) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1)), MARK(0)) ---------------------------------------- (144) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, tt)) -> c45(A__PLUS(mark(x0), tt), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1)), MARK(tt)) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1)), MARK(0)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, tt)) -> c45(A__PLUS(mark(x0), tt), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1)), MARK(tt)) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2, c43_1, c44_2, c44_1, c45_2 ---------------------------------------- (145) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (146) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c46_2, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2, c43_1, c44_2, c44_1, c45_2, c45_1 ---------------------------------------- (147) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(plus(z0, z1)) -> c46(A__PLUS(mark(z0), mark(z1)), MARK(z1)) by MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, tt)) -> c46(A__PLUS(mark(x0), tt), MARK(tt)) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) ---------------------------------------- (148) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, tt)) -> c46(A__PLUS(mark(x0), tt), MARK(tt)) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, tt)) -> c46(A__PLUS(mark(x0), tt), MARK(tt)) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2, c43_1, c44_2, c44_1, c45_2, c45_1, c46_2 ---------------------------------------- (149) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(plus(x0, tt)) -> c46(A__PLUS(mark(x0), tt), MARK(tt)) ---------------------------------------- (150) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0), MARK(0)) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2, c43_1, c44_2, c44_1, c45_2, c45_1, c46_2 ---------------------------------------- (151) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (152) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c48_2, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2, c43_1, c44_2, c44_1, c45_2, c45_1, c46_2, c46_1 ---------------------------------------- (153) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U71(z0, z1, z2)) -> c48(A__U71(mark(z0), z1, z2), MARK(z0)) by MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2), MARK(tt)) MARK(U71(s(z0), x1, x2)) -> c48(A__U71(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U71(0, x1, x2)) -> c48(A__U71(0, x1, x2), MARK(0)) ---------------------------------------- (154) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2), MARK(tt)) MARK(U71(s(z0), x1, x2)) -> c48(A__U71(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U71(0, x1, x2)) -> c48(A__U71(0, x1, x2), MARK(0)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2), MARK(tt)) MARK(U71(s(z0), x1, x2)) -> c48(A__U71(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U71(0, x1, x2)) -> c48(A__U71(0, x1, x2), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2, c43_1, c44_2, c44_1, c45_2, c45_1, c46_2, c46_1, c48_2 ---------------------------------------- (155) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U71(0, x1, x2)) -> c48(A__U71(0, x1, x2), MARK(0)) ---------------------------------------- (156) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2), MARK(tt)) MARK(U71(s(z0), x1, x2)) -> c48(A__U71(s(mark(z0)), x1, x2), MARK(s(z0))) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2), MARK(tt)) MARK(U71(s(z0), x1, x2)) -> c48(A__U71(s(mark(z0)), x1, x2), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2, c43_1, c44_2, c44_1, c45_2, c45_1, c46_2, c46_1, c48_2 ---------------------------------------- (157) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (158) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c49_2, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2, c43_1, c44_2, c44_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1 ---------------------------------------- (159) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(U72(z0, z1, z2)) -> c49(A__U72(mark(z0), z1, z2), MARK(z0)) by MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2), MARK(tt)) MARK(U72(s(z0), x1, x2)) -> c49(A__U72(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U72(0, x1, x2)) -> c49(A__U72(0, x1, x2), MARK(0)) ---------------------------------------- (160) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, 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c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2), MARK(tt)) MARK(U72(s(z0), x1, x2)) -> c49(A__U72(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U72(0, x1, x2)) -> c49(A__U72(0, x1, x2), MARK(0)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2), MARK(tt)) MARK(U72(s(z0), x1, x2)) -> c49(A__U72(s(mark(z0)), x1, x2), MARK(s(z0))) MARK(U72(0, x1, x2)) -> c49(A__U72(0, x1, x2), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2, c43_1, c44_2, c44_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c49_2 ---------------------------------------- (161) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(U72(0, x1, x2)) -> c49(A__U72(0, x1, x2), MARK(0)) ---------------------------------------- (162) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2), MARK(tt)) MARK(U72(s(z0), x1, x2)) -> c49(A__U72(s(mark(z0)), x1, x2), MARK(s(z0))) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2), MARK(tt)) MARK(U72(s(z0), x1, x2)) -> c49(A__U72(s(mark(z0)), x1, x2), MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2, c43_1, c44_2, c44_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c49_2 ---------------------------------------- (163) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 2 trailing tuple parts ---------------------------------------- (164) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), 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c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> 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MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c50_2, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2, c43_1, c44_2, c44_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c49_2, c49_1 ---------------------------------------- (165) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(x(z0, z1)) -> c50(A__X(mark(z0), mark(z1)), MARK(z0)) by MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, tt)) -> c50(A__X(mark(x0), tt), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1)), MARK(tt)) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1)), MARK(0)) ---------------------------------------- (166) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, tt)) -> c50(A__X(mark(x0), tt), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1)), MARK(tt)) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1)), MARK(0)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, tt)) -> c50(A__X(mark(x0), tt), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1)), MARK(tt)) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2, c43_1, c44_2, c44_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c49_2, c49_1, c50_2 ---------------------------------------- (167) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (168) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), 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MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), 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c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c51_2, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2, c43_1, c44_2, c44_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c49_2, c49_1, c50_2, c50_1 ---------------------------------------- (169) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace MARK(x(z0, z1)) -> c51(A__X(mark(z0), mark(z1)), MARK(z1)) by MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, tt)) -> c51(A__X(mark(x0), tt), MARK(tt)) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0), MARK(0)) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) ---------------------------------------- (170) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, 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MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, tt)) -> c51(A__X(mark(x0), tt), MARK(tt)) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0), MARK(0)) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), 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c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, tt)) -> c51(A__X(mark(x0), tt), MARK(tt)) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0), MARK(0)) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2, c43_1, c44_2, c44_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c49_2, c49_1, c50_2, c50_1, c51_2 ---------------------------------------- (171) CdtLeafRemovalProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing nodes: MARK(x(x0, tt)) -> c51(A__X(mark(x0), tt), MARK(tt)) ---------------------------------------- (172) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, 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MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0), MARK(0)) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0), MARK(0)) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2, c43_1, c44_2, c44_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c49_2, c49_1, c50_2, c50_1, c51_2 ---------------------------------------- (173) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (174) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), 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MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, 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a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> 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mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2, c43_1, c44_2, c44_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c49_2, c49_1, c50_2, c50_1, c51_2, c51_1 ---------------------------------------- (175) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U51(tt, x0, plus(z0, z1)) -> c12(A__U52(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) by A__U51(tt, x0, plus(x1, z1)) -> c12(A__U52(U11(a__isNat(x1), z1), x0, plus(x1, z1)), A__ISNAT(plus(x1, z1))) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) ---------------------------------------- (176) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, 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z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(x1, z1)) -> c12(A__U52(U11(a__isNat(x1), z1), x0, plus(x1, z1)), A__ISNAT(plus(x1, z1))) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(x1, z1)) -> c12(A__U52(U11(a__isNat(x1), z1), x0, plus(x1, z1)), A__ISNAT(plus(x1, z1))) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2, c43_1, c44_2, c44_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c49_2, c49_1, c50_2, c50_1, c51_2, c51_1 ---------------------------------------- (177) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (178) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) 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c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2, c43_1, c44_2, c44_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c49_2, c49_1, c50_2, c50_1, c51_2, c51_1 ---------------------------------------- (179) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) by A__U51(tt, x0, s(x1)) -> c12(A__U52(U21(a__isNat(x1)), x0, s(x1)), A__ISNAT(s(x1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) ---------------------------------------- (180) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) A__U51(tt, x0, s(x1)) -> c12(A__U52(U21(a__isNat(x1)), x0, s(x1)), A__ISNAT(s(x1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) A__U51(tt, x0, s(x1)) -> c12(A__U52(U21(a__isNat(x1)), x0, s(x1)), A__ISNAT(s(x1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2, c43_1, c44_2, c44_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c49_2, c49_1, c50_2, c50_1, c51_2, c51_1 ---------------------------------------- (181) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (182) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, s(x1)) -> c12(A__ISNAT(s(x1))) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), 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MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, 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a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, s(x1)) -> c12(A__ISNAT(s(x1))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_2, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2, c43_1, c44_2, c44_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c49_2, c49_1, c50_2, c50_1, c51_2, c51_1 ---------------------------------------- (183) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U51(tt, x0, x(z0, z1)) -> c12(A__U52(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) by A__U51(tt, x0, x(x1, z1)) -> c12(A__U52(U31(a__isNat(x1), z1), x0, x(x1, z1)), A__ISNAT(x(x1, z1))) A__U51(tt, x0, x(0, x2)) -> c12(A__U52(a__U31(tt, x2), x0, x(0, x2)), A__ISNAT(x(0, x2))) A__U51(tt, x0, x(plus(z0, z1), x2)) -> c12(A__U52(a__U31(a__U11(a__isNat(z0), z1), x2), x0, x(plus(z0, z1), x2)), A__ISNAT(x(plus(z0, z1), x2))) A__U51(tt, x0, x(s(z0), x2)) -> c12(A__U52(a__U31(a__U21(a__isNat(z0)), x2), x0, x(s(z0), x2)), A__ISNAT(x(s(z0), x2))) A__U51(tt, x0, x(x(z0, z1), x2)) -> c12(A__U52(a__U31(a__U31(a__isNat(z0), z1), x2), x0, x(x(z0, z1), x2)), A__ISNAT(x(x(z0, z1), x2))) A__U51(tt, x0, x(z0, x2)) -> c12(A__U52(a__U31(isNat(z0), x2), x0, x(z0, x2)), A__ISNAT(x(z0, x2))) ---------------------------------------- (184) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, s(x1)) -> c12(A__ISNAT(s(x1))) A__U51(tt, x0, x(x1, z1)) -> c12(A__U52(U31(a__isNat(x1), z1), x0, x(x1, z1)), A__ISNAT(x(x1, z1))) A__U51(tt, x0, x(0, x2)) -> c12(A__U52(a__U31(tt, x2), x0, x(0, x2)), A__ISNAT(x(0, x2))) A__U51(tt, x0, x(plus(z0, z1), x2)) -> c12(A__U52(a__U31(a__U11(a__isNat(z0), z1), x2), x0, x(plus(z0, z1), x2)), A__ISNAT(x(plus(z0, z1), x2))) A__U51(tt, x0, x(s(z0), x2)) -> c12(A__U52(a__U31(a__U21(a__isNat(z0)), x2), x0, x(s(z0), x2)), A__ISNAT(x(s(z0), x2))) A__U51(tt, x0, x(x(z0, z1), x2)) -> c12(A__U52(a__U31(a__U31(a__isNat(z0), z1), x2), x0, x(x(z0, z1), x2)), A__ISNAT(x(x(z0, z1), x2))) A__U51(tt, x0, x(z0, x2)) -> c12(A__U52(a__U31(isNat(z0), x2), x0, x(z0, x2)), A__ISNAT(x(z0, x2))) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), 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MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, s(x1)) -> c12(A__ISNAT(s(x1))) A__U51(tt, x0, x(x1, z1)) -> c12(A__U52(U31(a__isNat(x1), z1), x0, x(x1, z1)), A__ISNAT(x(x1, z1))) A__U51(tt, x0, x(0, x2)) -> c12(A__U52(a__U31(tt, x2), x0, x(0, x2)), A__ISNAT(x(0, x2))) A__U51(tt, x0, x(plus(z0, z1), x2)) -> c12(A__U52(a__U31(a__U11(a__isNat(z0), z1), x2), x0, x(plus(z0, z1), x2)), A__ISNAT(x(plus(z0, z1), x2))) A__U51(tt, x0, x(s(z0), x2)) -> c12(A__U52(a__U31(a__U21(a__isNat(z0)), x2), x0, x(s(z0), x2)), A__ISNAT(x(s(z0), x2))) A__U51(tt, x0, x(x(z0, z1), x2)) -> c12(A__U52(a__U31(a__U31(a__isNat(z0), z1), x2), x0, x(x(z0, z1), x2)), A__ISNAT(x(x(z0, z1), x2))) A__U51(tt, x0, x(z0, x2)) -> c12(A__U52(a__U31(isNat(z0), x2), x0, x(z0, x2)), A__ISNAT(x(z0, x2))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2, c43_1, c44_2, c44_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c49_2, c49_1, c50_2, c50_1, c51_2, c51_1, c12_2 ---------------------------------------- (185) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 1 trailing tuple parts ---------------------------------------- (186) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, s(x1)) -> c12(A__ISNAT(s(x1))) A__U51(tt, x0, x(0, x2)) -> c12(A__U52(a__U31(tt, x2), x0, x(0, x2)), A__ISNAT(x(0, x2))) A__U51(tt, x0, x(plus(z0, z1), x2)) -> c12(A__U52(a__U31(a__U11(a__isNat(z0), z1), x2), x0, x(plus(z0, z1), x2)), A__ISNAT(x(plus(z0, z1), x2))) A__U51(tt, x0, x(s(z0), x2)) -> c12(A__U52(a__U31(a__U21(a__isNat(z0)), x2), x0, x(s(z0), x2)), A__ISNAT(x(s(z0), x2))) A__U51(tt, x0, x(x(z0, z1), x2)) -> c12(A__U52(a__U31(a__U31(a__isNat(z0), z1), x2), x0, x(x(z0, z1), x2)), A__ISNAT(x(x(z0, z1), x2))) A__U51(tt, x0, x(z0, x2)) -> c12(A__U52(a__U31(isNat(z0), x2), x0, x(z0, x2)), A__ISNAT(x(z0, x2))) A__U51(tt, x0, x(x1, z1)) -> c12(A__ISNAT(x(x1, z1))) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, s(x1)) -> c12(A__ISNAT(s(x1))) A__U51(tt, x0, x(0, x2)) -> c12(A__U52(a__U31(tt, x2), x0, x(0, x2)), A__ISNAT(x(0, x2))) A__U51(tt, x0, x(plus(z0, z1), x2)) -> c12(A__U52(a__U31(a__U11(a__isNat(z0), z1), x2), x0, x(plus(z0, z1), x2)), A__ISNAT(x(plus(z0, z1), x2))) A__U51(tt, x0, x(s(z0), x2)) -> c12(A__U52(a__U31(a__U21(a__isNat(z0)), x2), x0, x(s(z0), x2)), A__ISNAT(x(s(z0), x2))) A__U51(tt, x0, x(x(z0, z1), x2)) -> c12(A__U52(a__U31(a__U31(a__isNat(z0), z1), x2), x0, x(x(z0, z1), x2)), A__ISNAT(x(x(z0, z1), x2))) A__U51(tt, x0, x(z0, x2)) -> c12(A__U52(a__U31(isNat(z0), x2), x0, x(z0, x2)), A__ISNAT(x(z0, x2))) A__U51(tt, x0, x(x1, z1)) -> c12(A__ISNAT(x(x1, z1))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2, c43_1, c44_2, c44_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c49_2, c49_1, c50_2, c50_1, c51_2, c51_1, c12_2 ---------------------------------------- (187) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U52(tt, U11(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(x1)) by A__U52(tt, U11(x0, z1), x2) -> c14(A__PLUS(mark(x2), U11(mark(x0), z1)), MARK(x2)) A__U52(tt, U11(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U11(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U52(tt, U11(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U52(tt, U11(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U11(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U11(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U11(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U11(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U11(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U11(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U11(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U11(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U11(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U11(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U11(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U11(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U11(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U11(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U11(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U11(x0, x1), tt) -> c14(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(tt)) A__U52(tt, U11(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U11(x0, x1), 0) -> c14(A__PLUS(0, a__U11(mark(x0), x1)), MARK(0)) ---------------------------------------- (188) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), 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MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> 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z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, s(x1)) -> c12(A__ISNAT(s(x1))) A__U51(tt, x0, x(0, x2)) -> c12(A__U52(a__U31(tt, x2), x0, x(0, x2)), A__ISNAT(x(0, x2))) A__U51(tt, x0, x(plus(z0, z1), x2)) -> c12(A__U52(a__U31(a__U11(a__isNat(z0), z1), x2), x0, x(plus(z0, z1), x2)), A__ISNAT(x(plus(z0, z1), x2))) A__U51(tt, x0, x(s(z0), x2)) -> c12(A__U52(a__U31(a__U21(a__isNat(z0)), x2), x0, x(s(z0), x2)), A__ISNAT(x(s(z0), x2))) A__U51(tt, x0, x(x(z0, z1), x2)) -> c12(A__U52(a__U31(a__U31(a__isNat(z0), z1), x2), x0, x(x(z0, z1), x2)), A__ISNAT(x(x(z0, z1), x2))) A__U51(tt, x0, x(z0, x2)) -> c12(A__U52(a__U31(isNat(z0), x2), x0, x(z0, x2)), A__ISNAT(x(z0, x2))) A__U51(tt, x0, x(x1, z1)) -> c12(A__ISNAT(x(x1, z1))) A__U52(tt, U11(x0, z1), x2) -> c14(A__PLUS(mark(x2), U11(mark(x0), z1)), MARK(x2)) A__U52(tt, U11(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U11(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U52(tt, U11(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U52(tt, U11(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U11(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U11(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U11(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U11(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U11(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U11(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U11(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U11(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U11(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U11(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U11(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U11(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U11(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U11(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U11(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U11(x0, x1), tt) -> c14(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(tt)) A__U52(tt, U11(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U11(x0, x1), 0) -> c14(A__PLUS(0, a__U11(mark(x0), x1)), MARK(0)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, s(x1)) -> c12(A__ISNAT(s(x1))) A__U51(tt, x0, x(0, x2)) -> c12(A__U52(a__U31(tt, x2), x0, x(0, x2)), A__ISNAT(x(0, x2))) A__U51(tt, x0, x(plus(z0, z1), x2)) -> c12(A__U52(a__U31(a__U11(a__isNat(z0), z1), x2), x0, x(plus(z0, z1), x2)), A__ISNAT(x(plus(z0, z1), x2))) A__U51(tt, x0, x(s(z0), x2)) -> c12(A__U52(a__U31(a__U21(a__isNat(z0)), x2), x0, x(s(z0), x2)), A__ISNAT(x(s(z0), x2))) A__U51(tt, x0, x(x(z0, z1), x2)) -> c12(A__U52(a__U31(a__U31(a__isNat(z0), z1), x2), x0, x(x(z0, z1), x2)), A__ISNAT(x(x(z0, z1), x2))) A__U51(tt, x0, x(z0, x2)) -> c12(A__U52(a__U31(isNat(z0), x2), x0, x(z0, x2)), A__ISNAT(x(z0, x2))) A__U51(tt, x0, x(x1, z1)) -> c12(A__ISNAT(x(x1, z1))) A__U52(tt, U11(x0, z1), x2) -> c14(A__PLUS(mark(x2), U11(mark(x0), z1)), MARK(x2)) A__U52(tt, U11(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U11(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U52(tt, U11(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U52(tt, U11(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U11(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U11(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U11(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U11(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U11(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U11(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U11(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U11(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U11(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U11(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U11(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U11(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U11(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U11(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U11(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U11(x0, x1), tt) -> c14(A__PLUS(tt, a__U11(mark(x0), x1)), MARK(tt)) A__U52(tt, U11(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U11(x0, x1), 0) -> c14(A__PLUS(0, a__U11(mark(x0), x1)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2, c43_1, c44_2, c44_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c49_2, c49_1, c50_2, c50_1, c51_2, c51_1, c12_2 ---------------------------------------- (189) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (190) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) 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c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, s(x1)) -> c12(A__ISNAT(s(x1))) A__U51(tt, x0, x(0, x2)) -> c12(A__U52(a__U31(tt, x2), x0, x(0, x2)), A__ISNAT(x(0, x2))) A__U51(tt, x0, x(plus(z0, z1), x2)) -> c12(A__U52(a__U31(a__U11(a__isNat(z0), z1), x2), x0, x(plus(z0, z1), x2)), A__ISNAT(x(plus(z0, z1), x2))) A__U51(tt, x0, x(s(z0), x2)) -> c12(A__U52(a__U31(a__U21(a__isNat(z0)), x2), x0, x(s(z0), x2)), A__ISNAT(x(s(z0), x2))) A__U51(tt, x0, x(x(z0, z1), x2)) -> c12(A__U52(a__U31(a__U31(a__isNat(z0), z1), x2), x0, x(x(z0, z1), x2)), A__ISNAT(x(x(z0, z1), x2))) A__U51(tt, x0, x(z0, x2)) -> c12(A__U52(a__U31(isNat(z0), x2), x0, x(z0, x2)), A__ISNAT(x(z0, x2))) A__U51(tt, x0, x(x1, z1)) -> c12(A__ISNAT(x(x1, z1))) A__U52(tt, U11(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U11(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U52(tt, U11(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U52(tt, U11(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U11(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U11(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U11(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U11(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U11(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U11(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U11(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U11(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U11(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U11(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U11(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U11(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U11(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U11(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U11(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U11(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U11(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U11(x0, x1), tt) -> c14(A__PLUS(tt, a__U11(mark(x0), x1))) A__U52(tt, U11(x0, x1), 0) -> c14(A__PLUS(0, a__U11(mark(x0), x1))) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, s(x1)) -> c12(A__ISNAT(s(x1))) A__U51(tt, x0, x(0, x2)) -> c12(A__U52(a__U31(tt, x2), x0, x(0, x2)), A__ISNAT(x(0, x2))) A__U51(tt, x0, x(plus(z0, z1), x2)) -> c12(A__U52(a__U31(a__U11(a__isNat(z0), z1), x2), x0, x(plus(z0, z1), x2)), A__ISNAT(x(plus(z0, z1), x2))) A__U51(tt, x0, x(s(z0), x2)) -> c12(A__U52(a__U31(a__U21(a__isNat(z0)), x2), x0, x(s(z0), x2)), A__ISNAT(x(s(z0), x2))) A__U51(tt, x0, x(x(z0, z1), x2)) -> c12(A__U52(a__U31(a__U31(a__isNat(z0), z1), x2), x0, x(x(z0, z1), x2)), A__ISNAT(x(x(z0, z1), x2))) A__U51(tt, x0, x(z0, x2)) -> c12(A__U52(a__U31(isNat(z0), x2), x0, x(z0, x2)), A__ISNAT(x(z0, x2))) A__U51(tt, x0, x(x1, z1)) -> c12(A__ISNAT(x(x1, z1))) A__U52(tt, U11(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U11(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U52(tt, U11(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U52(tt, U11(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U11(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U11(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U11(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U11(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U11(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U11(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U11(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U11(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U11(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U11(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U11(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U11(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U11(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U11(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U11(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U11(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U11(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U11(x0, x1), tt) -> c14(A__PLUS(tt, a__U11(mark(x0), x1))) A__U52(tt, U11(x0, x1), 0) -> c14(A__PLUS(0, a__U11(mark(x0), x1))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2, c43_1, c44_2, c44_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c49_2, c49_1, c50_2, c50_1, c51_2, c51_1, c12_2 ---------------------------------------- (191) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U52(tt, U12(z0), x1) -> c14(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(x1)) by A__U52(tt, U12(x0), x1) -> c14(A__PLUS(mark(x1), U12(mark(x0))), MARK(x1)) A__U52(tt, U12(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U12(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U52(tt, U12(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U12(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U12(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U12(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(tt), x1) -> c14(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U52(tt, U12(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U52(tt, U12(0), x1) -> c14(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U52(tt, U12(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U12(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U52(tt, U12(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U52(tt, U12(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U52(tt, U12(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U12(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U12(mark(x0))), MARK(U32(z0))) A__U52(tt, U12(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U12(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U12(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U12(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U12(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U12(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U12(mark(x0))), MARK(U61(z0))) A__U52(tt, U12(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U12(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U12(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U12(x0), tt) -> c14(A__PLUS(tt, a__U12(mark(x0))), MARK(tt)) A__U52(tt, U12(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U52(tt, U12(x0), 0) -> c14(A__PLUS(0, a__U12(mark(x0))), MARK(0)) ---------------------------------------- (192) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, s(x1)) -> c12(A__ISNAT(s(x1))) A__U51(tt, x0, x(0, x2)) -> c12(A__U52(a__U31(tt, x2), x0, x(0, x2)), A__ISNAT(x(0, x2))) A__U51(tt, x0, x(plus(z0, z1), x2)) -> c12(A__U52(a__U31(a__U11(a__isNat(z0), z1), x2), x0, x(plus(z0, z1), x2)), A__ISNAT(x(plus(z0, z1), x2))) A__U51(tt, x0, x(s(z0), x2)) -> c12(A__U52(a__U31(a__U21(a__isNat(z0)), x2), x0, x(s(z0), x2)), A__ISNAT(x(s(z0), x2))) A__U51(tt, x0, x(x(z0, z1), x2)) -> c12(A__U52(a__U31(a__U31(a__isNat(z0), z1), x2), x0, x(x(z0, z1), x2)), A__ISNAT(x(x(z0, z1), x2))) A__U51(tt, x0, x(z0, x2)) -> c12(A__U52(a__U31(isNat(z0), x2), x0, x(z0, x2)), A__ISNAT(x(z0, x2))) A__U51(tt, x0, x(x1, z1)) -> c12(A__ISNAT(x(x1, z1))) A__U52(tt, U11(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U11(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U52(tt, U11(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U52(tt, U11(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U11(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U11(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U11(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U11(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U11(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U11(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U11(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U11(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U11(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U11(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U11(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U11(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U11(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U11(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U11(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U11(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U11(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U11(x0, x1), tt) -> c14(A__PLUS(tt, a__U11(mark(x0), x1))) A__U52(tt, U11(x0, x1), 0) -> c14(A__PLUS(0, a__U11(mark(x0), x1))) A__U52(tt, U12(x0), x1) -> c14(A__PLUS(mark(x1), U12(mark(x0))), MARK(x1)) A__U52(tt, U12(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U12(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U52(tt, U12(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U12(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U12(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U12(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(tt), x1) -> c14(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U52(tt, U12(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U52(tt, U12(0), x1) -> c14(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U52(tt, U12(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U12(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U52(tt, U12(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U52(tt, U12(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U52(tt, U12(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U12(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U12(mark(x0))), MARK(U32(z0))) A__U52(tt, U12(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U12(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U12(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U12(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U12(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U12(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U12(mark(x0))), MARK(U61(z0))) A__U52(tt, U12(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U12(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U12(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U12(x0), tt) -> c14(A__PLUS(tt, a__U12(mark(x0))), MARK(tt)) A__U52(tt, U12(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U52(tt, U12(x0), 0) -> c14(A__PLUS(0, a__U12(mark(x0))), MARK(0)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, s(x1)) -> c12(A__ISNAT(s(x1))) A__U51(tt, x0, x(0, x2)) -> c12(A__U52(a__U31(tt, x2), x0, x(0, x2)), A__ISNAT(x(0, x2))) A__U51(tt, x0, x(plus(z0, z1), x2)) -> c12(A__U52(a__U31(a__U11(a__isNat(z0), z1), x2), x0, x(plus(z0, z1), x2)), A__ISNAT(x(plus(z0, z1), x2))) A__U51(tt, x0, x(s(z0), x2)) -> c12(A__U52(a__U31(a__U21(a__isNat(z0)), x2), x0, x(s(z0), x2)), A__ISNAT(x(s(z0), x2))) A__U51(tt, x0, x(x(z0, z1), x2)) -> c12(A__U52(a__U31(a__U31(a__isNat(z0), z1), x2), x0, x(x(z0, z1), x2)), A__ISNAT(x(x(z0, z1), x2))) A__U51(tt, x0, x(z0, x2)) -> c12(A__U52(a__U31(isNat(z0), x2), x0, x(z0, x2)), A__ISNAT(x(z0, x2))) A__U51(tt, x0, x(x1, z1)) -> c12(A__ISNAT(x(x1, z1))) A__U52(tt, U11(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U11(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U52(tt, U11(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U52(tt, U11(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U11(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U11(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U11(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U11(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U11(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U11(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U11(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U11(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U11(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U11(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U11(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U11(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U11(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U11(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U11(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U11(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U11(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U11(x0, x1), tt) -> c14(A__PLUS(tt, a__U11(mark(x0), x1))) A__U52(tt, U11(x0, x1), 0) -> c14(A__PLUS(0, a__U11(mark(x0), x1))) A__U52(tt, U12(x0), x1) -> c14(A__PLUS(mark(x1), U12(mark(x0))), MARK(x1)) A__U52(tt, U12(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U12(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U52(tt, U12(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U12(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U12(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U12(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(tt), x1) -> c14(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U52(tt, U12(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U52(tt, U12(0), x1) -> c14(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U52(tt, U12(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U12(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U52(tt, U12(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U52(tt, U12(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U52(tt, U12(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U12(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U12(mark(x0))), MARK(U32(z0))) A__U52(tt, U12(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U12(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U12(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U12(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U12(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U12(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U12(mark(x0))), MARK(U61(z0))) A__U52(tt, U12(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U12(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U12(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U12(x0), tt) -> c14(A__PLUS(tt, a__U12(mark(x0))), MARK(tt)) A__U52(tt, U12(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U52(tt, U12(x0), 0) -> c14(A__PLUS(0, a__U12(mark(x0))), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2, c43_1, c44_2, c44_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c49_2, c49_1, c50_2, c50_1, c51_2, c51_1, c12_2 ---------------------------------------- (193) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (194) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, s(x1)) -> c12(A__ISNAT(s(x1))) A__U51(tt, x0, x(0, x2)) -> c12(A__U52(a__U31(tt, x2), x0, x(0, x2)), A__ISNAT(x(0, x2))) A__U51(tt, x0, x(plus(z0, z1), x2)) -> c12(A__U52(a__U31(a__U11(a__isNat(z0), z1), x2), x0, x(plus(z0, z1), x2)), A__ISNAT(x(plus(z0, z1), x2))) A__U51(tt, x0, x(s(z0), x2)) -> c12(A__U52(a__U31(a__U21(a__isNat(z0)), x2), x0, x(s(z0), x2)), A__ISNAT(x(s(z0), x2))) A__U51(tt, x0, x(x(z0, z1), x2)) -> c12(A__U52(a__U31(a__U31(a__isNat(z0), z1), x2), x0, x(x(z0, z1), x2)), A__ISNAT(x(x(z0, z1), x2))) A__U51(tt, x0, x(z0, x2)) -> c12(A__U52(a__U31(isNat(z0), x2), x0, x(z0, x2)), A__ISNAT(x(z0, x2))) A__U51(tt, x0, x(x1, z1)) -> c12(A__ISNAT(x(x1, z1))) A__U52(tt, U11(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U11(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U52(tt, U11(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U52(tt, U11(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U11(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U11(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U11(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U11(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U11(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U11(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U11(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U11(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U11(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U11(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U11(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U11(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U11(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U11(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U11(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U11(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U11(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U11(x0, x1), tt) -> c14(A__PLUS(tt, a__U11(mark(x0), x1))) A__U52(tt, U11(x0, x1), 0) -> c14(A__PLUS(0, a__U11(mark(x0), x1))) A__U52(tt, U12(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U12(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U52(tt, U12(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U12(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U12(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U12(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(tt), x1) -> c14(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U52(tt, U12(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U52(tt, U12(0), x1) -> c14(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U52(tt, U12(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U12(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U52(tt, U12(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U52(tt, U12(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U52(tt, U12(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U12(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U12(mark(x0))), MARK(U32(z0))) A__U52(tt, U12(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U12(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U12(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U12(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U12(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U12(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U12(mark(x0))), MARK(U61(z0))) A__U52(tt, U12(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U12(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U12(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U12(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U52(tt, U12(x0), x1) -> c14(MARK(x1)) A__U52(tt, U12(x0), tt) -> c14(A__PLUS(tt, a__U12(mark(x0)))) A__U52(tt, U12(x0), 0) -> c14(A__PLUS(0, a__U12(mark(x0)))) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> 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MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, s(x1)) -> c12(A__ISNAT(s(x1))) A__U51(tt, x0, x(0, x2)) -> c12(A__U52(a__U31(tt, x2), x0, x(0, x2)), A__ISNAT(x(0, x2))) A__U51(tt, x0, x(plus(z0, z1), x2)) -> c12(A__U52(a__U31(a__U11(a__isNat(z0), z1), x2), x0, x(plus(z0, z1), x2)), A__ISNAT(x(plus(z0, z1), x2))) A__U51(tt, x0, x(s(z0), x2)) -> c12(A__U52(a__U31(a__U21(a__isNat(z0)), x2), x0, x(s(z0), x2)), A__ISNAT(x(s(z0), x2))) A__U51(tt, x0, x(x(z0, z1), x2)) -> c12(A__U52(a__U31(a__U31(a__isNat(z0), z1), x2), x0, x(x(z0, z1), x2)), A__ISNAT(x(x(z0, z1), x2))) A__U51(tt, x0, x(z0, x2)) -> c12(A__U52(a__U31(isNat(z0), x2), x0, x(z0, x2)), A__ISNAT(x(z0, x2))) A__U51(tt, x0, x(x1, z1)) -> c12(A__ISNAT(x(x1, z1))) A__U52(tt, U11(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U11(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U52(tt, U11(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U52(tt, U11(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U11(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U11(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U11(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U11(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U11(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U11(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U11(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U11(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U11(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U11(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U11(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U11(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U11(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U11(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U11(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U11(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U11(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U11(x0, x1), tt) -> c14(A__PLUS(tt, a__U11(mark(x0), x1))) A__U52(tt, U11(x0, x1), 0) -> c14(A__PLUS(0, a__U11(mark(x0), x1))) A__U52(tt, U12(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U12(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U52(tt, U12(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U12(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U12(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U12(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(tt), x1) -> c14(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U52(tt, U12(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U52(tt, U12(0), x1) -> c14(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U52(tt, U12(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U12(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U52(tt, U12(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U52(tt, U12(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U52(tt, U12(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U12(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U12(mark(x0))), MARK(U32(z0))) A__U52(tt, U12(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U12(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U12(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U12(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U12(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U12(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U12(mark(x0))), MARK(U61(z0))) A__U52(tt, U12(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U12(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U12(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U12(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U52(tt, U12(x0), x1) -> c14(MARK(x1)) A__U52(tt, U12(x0), tt) -> c14(A__PLUS(tt, a__U12(mark(x0)))) A__U52(tt, U12(x0), 0) -> c14(A__PLUS(0, a__U12(mark(x0)))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2, c43_1, c44_2, c44_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c49_2, c49_1, c50_2, c50_1, c51_2, c51_1, c12_2 ---------------------------------------- (195) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), a__isNat(z0)), MARK(x1)) by A__U52(tt, isNat(0), x1) -> c14(A__PLUS(mark(x1), tt), MARK(x1)) A__U52(tt, isNat(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U52(tt, isNat(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U31(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), isNat(z0)), MARK(x1)) A__U52(tt, isNat(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U52(tt, isNat(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U52(tt, isNat(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U52(tt, isNat(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U52(tt, isNat(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U52(tt, isNat(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__isNat(x0)), MARK(U32(z0))) A__U52(tt, isNat(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__isNat(x0)), MARK(U41(z0, z1))) A__U52(tt, isNat(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__isNat(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, isNat(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__isNat(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, isNat(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U52(tt, isNat(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__isNat(x0)), MARK(U61(z0))) A__U52(tt, isNat(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__isNat(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, isNat(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__isNat(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, isNat(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1))) A__U52(tt, isNat(x0), tt) -> c14(A__PLUS(tt, a__isNat(x0)), MARK(tt)) A__U52(tt, isNat(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U52(tt, isNat(x0), 0) -> c14(A__PLUS(0, a__isNat(x0)), MARK(0)) ---------------------------------------- (196) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> 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c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, s(x1)) -> c12(A__ISNAT(s(x1))) A__U51(tt, x0, x(0, x2)) -> c12(A__U52(a__U31(tt, x2), x0, x(0, x2)), A__ISNAT(x(0, x2))) A__U51(tt, x0, x(plus(z0, z1), x2)) -> c12(A__U52(a__U31(a__U11(a__isNat(z0), z1), x2), x0, x(plus(z0, z1), x2)), A__ISNAT(x(plus(z0, z1), x2))) A__U51(tt, x0, x(s(z0), x2)) -> c12(A__U52(a__U31(a__U21(a__isNat(z0)), x2), x0, x(s(z0), x2)), A__ISNAT(x(s(z0), x2))) A__U51(tt, x0, x(x(z0, z1), x2)) -> c12(A__U52(a__U31(a__U31(a__isNat(z0), z1), x2), x0, x(x(z0, z1), x2)), A__ISNAT(x(x(z0, z1), x2))) A__U51(tt, x0, x(z0, x2)) -> c12(A__U52(a__U31(isNat(z0), x2), x0, x(z0, x2)), A__ISNAT(x(z0, x2))) A__U51(tt, x0, x(x1, z1)) -> c12(A__ISNAT(x(x1, z1))) A__U52(tt, U11(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U11(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U52(tt, U11(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U52(tt, U11(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U11(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U11(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U11(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U11(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U11(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U11(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U11(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U11(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U11(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U11(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U11(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U11(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U11(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U11(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U11(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U11(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U11(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U11(x0, x1), tt) -> c14(A__PLUS(tt, a__U11(mark(x0), x1))) A__U52(tt, U11(x0, x1), 0) -> c14(A__PLUS(0, a__U11(mark(x0), x1))) A__U52(tt, U12(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U12(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U52(tt, U12(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U12(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U12(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U12(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(tt), x1) -> c14(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U52(tt, U12(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U52(tt, U12(0), x1) -> c14(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U52(tt, U12(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U12(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U52(tt, U12(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U52(tt, U12(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U52(tt, U12(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U12(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U12(mark(x0))), MARK(U32(z0))) A__U52(tt, U12(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U12(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U12(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U12(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U12(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U12(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U12(mark(x0))), MARK(U61(z0))) A__U52(tt, U12(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U12(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U12(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U12(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U52(tt, U12(x0), x1) -> c14(MARK(x1)) A__U52(tt, U12(x0), tt) -> c14(A__PLUS(tt, a__U12(mark(x0)))) A__U52(tt, U12(x0), 0) -> c14(A__PLUS(0, a__U12(mark(x0)))) A__U52(tt, isNat(0), x1) -> c14(A__PLUS(mark(x1), tt), MARK(x1)) A__U52(tt, isNat(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U52(tt, isNat(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U31(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), isNat(z0)), MARK(x1)) A__U52(tt, isNat(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U52(tt, isNat(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U52(tt, isNat(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U52(tt, isNat(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U52(tt, isNat(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U52(tt, isNat(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__isNat(x0)), MARK(U32(z0))) A__U52(tt, isNat(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__isNat(x0)), MARK(U41(z0, z1))) A__U52(tt, isNat(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__isNat(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, isNat(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__isNat(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, isNat(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U52(tt, isNat(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__isNat(x0)), MARK(U61(z0))) A__U52(tt, isNat(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__isNat(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, isNat(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__isNat(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, isNat(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1))) A__U52(tt, isNat(x0), tt) -> c14(A__PLUS(tt, a__isNat(x0)), MARK(tt)) A__U52(tt, isNat(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U52(tt, isNat(x0), 0) -> c14(A__PLUS(0, a__isNat(x0)), MARK(0)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, s(x1)) -> c12(A__ISNAT(s(x1))) A__U51(tt, x0, x(0, x2)) -> c12(A__U52(a__U31(tt, x2), x0, x(0, x2)), A__ISNAT(x(0, x2))) A__U51(tt, x0, x(plus(z0, z1), x2)) -> c12(A__U52(a__U31(a__U11(a__isNat(z0), z1), x2), x0, x(plus(z0, z1), x2)), A__ISNAT(x(plus(z0, z1), x2))) A__U51(tt, x0, x(s(z0), x2)) -> c12(A__U52(a__U31(a__U21(a__isNat(z0)), x2), x0, x(s(z0), x2)), A__ISNAT(x(s(z0), x2))) A__U51(tt, x0, x(x(z0, z1), x2)) -> c12(A__U52(a__U31(a__U31(a__isNat(z0), z1), x2), x0, x(x(z0, z1), x2)), A__ISNAT(x(x(z0, z1), x2))) A__U51(tt, x0, x(z0, x2)) -> c12(A__U52(a__U31(isNat(z0), x2), x0, x(z0, x2)), A__ISNAT(x(z0, x2))) A__U51(tt, x0, x(x1, z1)) -> c12(A__ISNAT(x(x1, z1))) A__U52(tt, U11(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U11(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U52(tt, U11(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U52(tt, U11(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U11(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U11(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U11(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U11(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U11(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U11(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U11(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U11(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U11(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U11(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U11(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U11(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U11(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U11(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U11(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U11(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U11(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U11(x0, x1), tt) -> c14(A__PLUS(tt, a__U11(mark(x0), x1))) A__U52(tt, U11(x0, x1), 0) -> c14(A__PLUS(0, a__U11(mark(x0), x1))) A__U52(tt, U12(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U12(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U52(tt, U12(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U12(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U12(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U12(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(tt), x1) -> c14(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U52(tt, U12(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U52(tt, U12(0), x1) -> c14(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U52(tt, U12(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U12(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U52(tt, U12(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U52(tt, U12(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U52(tt, U12(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U12(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U12(mark(x0))), MARK(U32(z0))) A__U52(tt, U12(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U12(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U12(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U12(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U12(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U12(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U12(mark(x0))), MARK(U61(z0))) A__U52(tt, U12(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U12(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U12(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U12(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U52(tt, U12(x0), x1) -> c14(MARK(x1)) A__U52(tt, U12(x0), tt) -> c14(A__PLUS(tt, a__U12(mark(x0)))) A__U52(tt, U12(x0), 0) -> c14(A__PLUS(0, a__U12(mark(x0)))) A__U52(tt, isNat(0), x1) -> c14(A__PLUS(mark(x1), tt), MARK(x1)) A__U52(tt, isNat(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U52(tt, isNat(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U31(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(A__PLUS(mark(x1), isNat(z0)), MARK(x1)) A__U52(tt, isNat(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U52(tt, isNat(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U52(tt, isNat(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U52(tt, isNat(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U52(tt, isNat(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U52(tt, isNat(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__isNat(x0)), MARK(U32(z0))) A__U52(tt, isNat(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__isNat(x0)), MARK(U41(z0, z1))) A__U52(tt, isNat(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__isNat(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, isNat(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__isNat(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, isNat(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U52(tt, isNat(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__isNat(x0)), MARK(U61(z0))) A__U52(tt, isNat(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__isNat(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, isNat(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__isNat(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, isNat(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1))) A__U52(tt, isNat(x0), tt) -> c14(A__PLUS(tt, a__isNat(x0)), MARK(tt)) A__U52(tt, isNat(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U52(tt, isNat(x0), 0) -> c14(A__PLUS(0, a__isNat(x0)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2, c43_1, c44_2, c44_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c49_2, c49_1, c50_2, c50_1, c51_2, c51_1, c12_2 ---------------------------------------- (197) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 4 trailing tuple parts ---------------------------------------- (198) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) 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MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, s(x1)) -> c12(A__ISNAT(s(x1))) A__U51(tt, x0, x(0, x2)) -> c12(A__U52(a__U31(tt, x2), x0, x(0, x2)), A__ISNAT(x(0, x2))) A__U51(tt, x0, x(plus(z0, z1), x2)) -> c12(A__U52(a__U31(a__U11(a__isNat(z0), z1), x2), x0, x(plus(z0, z1), x2)), A__ISNAT(x(plus(z0, z1), x2))) A__U51(tt, x0, x(s(z0), x2)) -> c12(A__U52(a__U31(a__U21(a__isNat(z0)), x2), x0, x(s(z0), x2)), A__ISNAT(x(s(z0), x2))) A__U51(tt, x0, x(x(z0, z1), x2)) -> c12(A__U52(a__U31(a__U31(a__isNat(z0), z1), x2), x0, x(x(z0, z1), x2)), A__ISNAT(x(x(z0, z1), x2))) A__U51(tt, x0, x(z0, x2)) -> c12(A__U52(a__U31(isNat(z0), x2), x0, x(z0, x2)), A__ISNAT(x(z0, x2))) A__U51(tt, x0, x(x1, z1)) -> c12(A__ISNAT(x(x1, z1))) A__U52(tt, U11(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U11(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U52(tt, U11(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U52(tt, U11(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U11(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U11(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U11(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U11(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U11(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U11(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U11(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U11(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U11(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U11(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U11(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U11(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U11(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U11(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U11(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U11(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U11(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U11(x0, x1), tt) -> c14(A__PLUS(tt, a__U11(mark(x0), x1))) A__U52(tt, U11(x0, x1), 0) -> c14(A__PLUS(0, a__U11(mark(x0), x1))) A__U52(tt, U12(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U12(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U52(tt, U12(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U12(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U12(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U12(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(tt), x1) -> c14(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U52(tt, U12(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U52(tt, U12(0), x1) -> c14(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U52(tt, U12(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U12(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U52(tt, U12(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U52(tt, U12(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U52(tt, U12(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U12(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U12(mark(x0))), MARK(U32(z0))) A__U52(tt, U12(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U12(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U12(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U12(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U12(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U12(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U12(mark(x0))), MARK(U61(z0))) A__U52(tt, U12(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U12(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U12(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U12(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U52(tt, U12(x0), x1) -> c14(MARK(x1)) A__U52(tt, U12(x0), tt) -> c14(A__PLUS(tt, a__U12(mark(x0)))) A__U52(tt, U12(x0), 0) -> c14(A__PLUS(0, a__U12(mark(x0)))) A__U52(tt, isNat(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U52(tt, isNat(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U31(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U52(tt, isNat(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U52(tt, isNat(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U52(tt, isNat(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U52(tt, isNat(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U52(tt, isNat(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__isNat(x0)), MARK(U32(z0))) A__U52(tt, isNat(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__isNat(x0)), MARK(U41(z0, z1))) A__U52(tt, isNat(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__isNat(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, isNat(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__isNat(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, isNat(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U52(tt, isNat(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__isNat(x0)), MARK(U61(z0))) A__U52(tt, isNat(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__isNat(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, isNat(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__isNat(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, isNat(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1))) A__U52(tt, isNat(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U52(tt, isNat(0), x1) -> c14(MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(MARK(x1)) A__U52(tt, isNat(x0), tt) -> c14(A__PLUS(tt, a__isNat(x0))) A__U52(tt, isNat(x0), 0) -> c14(A__PLUS(0, a__isNat(x0))) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, s(x1)) -> c12(A__ISNAT(s(x1))) A__U51(tt, x0, x(0, x2)) -> c12(A__U52(a__U31(tt, x2), x0, x(0, x2)), A__ISNAT(x(0, x2))) A__U51(tt, x0, x(plus(z0, z1), x2)) -> c12(A__U52(a__U31(a__U11(a__isNat(z0), z1), x2), x0, x(plus(z0, z1), x2)), A__ISNAT(x(plus(z0, z1), x2))) A__U51(tt, x0, x(s(z0), x2)) -> c12(A__U52(a__U31(a__U21(a__isNat(z0)), x2), x0, x(s(z0), x2)), A__ISNAT(x(s(z0), x2))) A__U51(tt, x0, x(x(z0, z1), x2)) -> c12(A__U52(a__U31(a__U31(a__isNat(z0), z1), x2), x0, x(x(z0, z1), x2)), A__ISNAT(x(x(z0, z1), x2))) A__U51(tt, x0, x(z0, x2)) -> c12(A__U52(a__U31(isNat(z0), x2), x0, x(z0, x2)), A__ISNAT(x(z0, x2))) A__U51(tt, x0, x(x1, z1)) -> c12(A__ISNAT(x(x1, z1))) A__U52(tt, U11(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U11(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U52(tt, U11(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U52(tt, U11(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U11(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U11(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U11(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U11(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U11(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U11(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U11(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U11(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U11(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U11(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U11(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U11(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U11(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U11(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U11(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U11(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U11(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U11(x0, x1), tt) -> c14(A__PLUS(tt, a__U11(mark(x0), x1))) A__U52(tt, U11(x0, x1), 0) -> c14(A__PLUS(0, a__U11(mark(x0), x1))) A__U52(tt, U12(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U12(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U52(tt, U12(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U12(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U12(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U12(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(tt), x1) -> c14(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U52(tt, U12(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U52(tt, U12(0), x1) -> c14(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U52(tt, U12(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U12(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U52(tt, U12(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U52(tt, U12(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U52(tt, U12(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U12(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U12(mark(x0))), MARK(U32(z0))) A__U52(tt, U12(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U12(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U12(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U12(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U12(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U12(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U12(mark(x0))), MARK(U61(z0))) A__U52(tt, U12(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U12(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U12(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U12(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U52(tt, U12(x0), x1) -> c14(MARK(x1)) A__U52(tt, U12(x0), tt) -> c14(A__PLUS(tt, a__U12(mark(x0)))) A__U52(tt, U12(x0), 0) -> c14(A__PLUS(0, a__U12(mark(x0)))) A__U52(tt, isNat(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U52(tt, isNat(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U31(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U52(tt, isNat(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U52(tt, isNat(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U52(tt, isNat(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U52(tt, isNat(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U52(tt, isNat(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__isNat(x0)), MARK(U32(z0))) A__U52(tt, isNat(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__isNat(x0)), MARK(U41(z0, z1))) A__U52(tt, isNat(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__isNat(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, isNat(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__isNat(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, isNat(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U52(tt, isNat(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__isNat(x0)), MARK(U61(z0))) A__U52(tt, isNat(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__isNat(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, isNat(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__isNat(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, isNat(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1))) A__U52(tt, isNat(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U52(tt, isNat(0), x1) -> c14(MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(MARK(x1)) A__U52(tt, isNat(x0), tt) -> c14(A__PLUS(tt, a__isNat(x0))) A__U52(tt, isNat(x0), 0) -> c14(A__PLUS(0, a__isNat(x0))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2, c43_1, c44_2, c44_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c49_2, c49_1, c50_2, c50_1, c51_2, c51_1, c12_2 ---------------------------------------- (199) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U52(tt, U21(z0), x1) -> c14(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(x1)) by A__U52(tt, U21(x0), x1) -> c14(A__PLUS(mark(x1), U21(mark(x0))), MARK(x1)) A__U52(tt, U21(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U21(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U52(tt, U21(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U21(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U21(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U21(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U21(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U21(tt), x1) -> c14(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U52(tt, U21(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U52(tt, U21(0), x1) -> c14(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U52(tt, U21(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U21(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U52(tt, U21(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U52(tt, U21(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U52(tt, U21(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U21(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U21(mark(x0))), MARK(U32(z0))) A__U52(tt, U21(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U21(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U21(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U21(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U21(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U21(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U21(mark(x0))), MARK(U61(z0))) A__U52(tt, U21(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U21(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U21(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U21(x0), tt) -> c14(A__PLUS(tt, a__U21(mark(x0))), MARK(tt)) A__U52(tt, U21(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U52(tt, U21(x0), 0) -> c14(A__PLUS(0, a__U21(mark(x0))), MARK(0)) ---------------------------------------- (200) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, s(x1)) -> c12(A__ISNAT(s(x1))) A__U51(tt, x0, x(0, x2)) -> c12(A__U52(a__U31(tt, x2), x0, x(0, x2)), A__ISNAT(x(0, x2))) A__U51(tt, x0, x(plus(z0, z1), x2)) -> c12(A__U52(a__U31(a__U11(a__isNat(z0), z1), x2), x0, x(plus(z0, z1), x2)), A__ISNAT(x(plus(z0, z1), x2))) A__U51(tt, x0, x(s(z0), x2)) -> c12(A__U52(a__U31(a__U21(a__isNat(z0)), x2), x0, x(s(z0), x2)), A__ISNAT(x(s(z0), x2))) A__U51(tt, x0, x(x(z0, z1), x2)) -> c12(A__U52(a__U31(a__U31(a__isNat(z0), z1), x2), x0, x(x(z0, z1), x2)), A__ISNAT(x(x(z0, z1), x2))) A__U51(tt, x0, x(z0, x2)) -> c12(A__U52(a__U31(isNat(z0), x2), x0, x(z0, x2)), A__ISNAT(x(z0, x2))) A__U51(tt, x0, x(x1, z1)) -> c12(A__ISNAT(x(x1, z1))) A__U52(tt, U11(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U11(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U52(tt, U11(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U52(tt, U11(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U11(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U11(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U11(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U11(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U11(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U11(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U11(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U11(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U11(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U11(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U11(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U11(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U11(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U11(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U11(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U11(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U11(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U11(x0, x1), tt) -> c14(A__PLUS(tt, a__U11(mark(x0), x1))) A__U52(tt, U11(x0, x1), 0) -> c14(A__PLUS(0, a__U11(mark(x0), x1))) A__U52(tt, U12(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U12(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U52(tt, U12(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U12(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U12(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U12(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(tt), x1) -> c14(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U52(tt, U12(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U52(tt, U12(0), x1) -> c14(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U52(tt, U12(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U12(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U52(tt, U12(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U52(tt, U12(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U52(tt, U12(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U12(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U12(mark(x0))), MARK(U32(z0))) A__U52(tt, U12(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U12(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U12(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U12(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U12(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U12(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U12(mark(x0))), MARK(U61(z0))) A__U52(tt, U12(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U12(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U12(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U12(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U52(tt, U12(x0), x1) -> c14(MARK(x1)) A__U52(tt, U12(x0), tt) -> c14(A__PLUS(tt, a__U12(mark(x0)))) A__U52(tt, U12(x0), 0) -> c14(A__PLUS(0, a__U12(mark(x0)))) A__U52(tt, isNat(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U52(tt, isNat(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U31(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U52(tt, isNat(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U52(tt, isNat(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U52(tt, isNat(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U52(tt, isNat(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U52(tt, isNat(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__isNat(x0)), MARK(U32(z0))) A__U52(tt, isNat(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__isNat(x0)), MARK(U41(z0, z1))) A__U52(tt, isNat(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__isNat(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, isNat(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__isNat(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, isNat(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U52(tt, isNat(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__isNat(x0)), MARK(U61(z0))) A__U52(tt, isNat(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__isNat(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, isNat(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__isNat(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, isNat(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1))) A__U52(tt, isNat(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U52(tt, isNat(0), x1) -> c14(MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(MARK(x1)) A__U52(tt, isNat(x0), tt) -> c14(A__PLUS(tt, a__isNat(x0))) A__U52(tt, isNat(x0), 0) -> c14(A__PLUS(0, a__isNat(x0))) A__U52(tt, U21(x0), x1) -> c14(A__PLUS(mark(x1), U21(mark(x0))), MARK(x1)) A__U52(tt, U21(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U21(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U52(tt, U21(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U21(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U21(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U21(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U21(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U21(tt), x1) -> c14(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U52(tt, U21(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U52(tt, U21(0), x1) -> c14(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U52(tt, U21(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U21(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U52(tt, U21(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U52(tt, U21(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U52(tt, U21(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U21(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U21(mark(x0))), MARK(U32(z0))) A__U52(tt, U21(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U21(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U21(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U21(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U21(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U21(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U21(mark(x0))), MARK(U61(z0))) A__U52(tt, U21(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U21(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U21(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U21(x0), tt) -> c14(A__PLUS(tt, a__U21(mark(x0))), MARK(tt)) A__U52(tt, U21(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U52(tt, U21(x0), 0) -> c14(A__PLUS(0, a__U21(mark(x0))), MARK(0)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, 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MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, 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MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) 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c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, s(x1)) -> c12(A__ISNAT(s(x1))) A__U51(tt, x0, x(0, x2)) -> c12(A__U52(a__U31(tt, x2), x0, x(0, x2)), A__ISNAT(x(0, x2))) A__U51(tt, x0, x(plus(z0, z1), x2)) -> c12(A__U52(a__U31(a__U11(a__isNat(z0), z1), x2), x0, x(plus(z0, z1), x2)), A__ISNAT(x(plus(z0, z1), x2))) A__U51(tt, x0, x(s(z0), x2)) -> c12(A__U52(a__U31(a__U21(a__isNat(z0)), x2), x0, x(s(z0), x2)), A__ISNAT(x(s(z0), x2))) A__U51(tt, x0, x(x(z0, z1), x2)) -> c12(A__U52(a__U31(a__U31(a__isNat(z0), z1), x2), x0, x(x(z0, z1), x2)), A__ISNAT(x(x(z0, z1), x2))) A__U51(tt, x0, x(z0, x2)) -> c12(A__U52(a__U31(isNat(z0), x2), x0, x(z0, x2)), A__ISNAT(x(z0, x2))) A__U51(tt, x0, x(x1, z1)) -> c12(A__ISNAT(x(x1, z1))) A__U52(tt, U11(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U11(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U52(tt, U11(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U52(tt, U11(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U11(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U11(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U11(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U11(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U11(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U11(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U11(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U11(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U11(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U11(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U11(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U11(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U11(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U11(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U11(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U11(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U11(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U11(x0, x1), tt) -> c14(A__PLUS(tt, a__U11(mark(x0), x1))) A__U52(tt, U11(x0, x1), 0) -> c14(A__PLUS(0, a__U11(mark(x0), x1))) A__U52(tt, U12(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U12(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U52(tt, U12(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U12(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U12(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U12(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(tt), x1) -> c14(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U52(tt, U12(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U52(tt, U12(0), x1) -> c14(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U52(tt, U12(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U12(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U52(tt, U12(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U52(tt, U12(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U52(tt, U12(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U12(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U12(mark(x0))), MARK(U32(z0))) A__U52(tt, U12(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U12(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U12(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U12(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U12(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U12(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U12(mark(x0))), MARK(U61(z0))) A__U52(tt, U12(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U12(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U12(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U12(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U52(tt, U12(x0), x1) -> c14(MARK(x1)) A__U52(tt, U12(x0), tt) -> c14(A__PLUS(tt, a__U12(mark(x0)))) A__U52(tt, U12(x0), 0) -> c14(A__PLUS(0, a__U12(mark(x0)))) A__U52(tt, isNat(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U52(tt, isNat(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U31(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U52(tt, isNat(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U52(tt, isNat(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U52(tt, isNat(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U52(tt, isNat(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U52(tt, isNat(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__isNat(x0)), MARK(U32(z0))) A__U52(tt, isNat(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__isNat(x0)), MARK(U41(z0, z1))) A__U52(tt, isNat(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__isNat(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, isNat(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__isNat(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, isNat(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U52(tt, isNat(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__isNat(x0)), MARK(U61(z0))) A__U52(tt, isNat(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__isNat(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, isNat(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__isNat(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, isNat(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1))) A__U52(tt, isNat(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U52(tt, isNat(0), x1) -> c14(MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(MARK(x1)) A__U52(tt, isNat(x0), tt) -> c14(A__PLUS(tt, a__isNat(x0))) A__U52(tt, isNat(x0), 0) -> c14(A__PLUS(0, a__isNat(x0))) A__U52(tt, U21(x0), x1) -> c14(A__PLUS(mark(x1), U21(mark(x0))), MARK(x1)) A__U52(tt, U21(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U21(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U52(tt, U21(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U21(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U21(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U21(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U21(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U21(tt), x1) -> c14(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U52(tt, U21(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U52(tt, U21(0), x1) -> c14(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U52(tt, U21(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U21(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U52(tt, U21(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U52(tt, U21(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U52(tt, U21(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U21(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U21(mark(x0))), MARK(U32(z0))) A__U52(tt, U21(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U21(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U21(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U21(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U21(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U21(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U21(mark(x0))), MARK(U61(z0))) A__U52(tt, U21(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U21(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U21(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U21(x0), tt) -> c14(A__PLUS(tt, a__U21(mark(x0))), MARK(tt)) A__U52(tt, U21(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U52(tt, U21(x0), 0) -> c14(A__PLUS(0, a__U21(mark(x0))), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2, c43_1, c44_2, c44_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c49_2, c49_1, c50_2, c50_1, c51_2, c51_1, c12_2 ---------------------------------------- (201) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (202) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, s(x1)) -> c12(A__ISNAT(s(x1))) A__U51(tt, x0, x(0, x2)) -> c12(A__U52(a__U31(tt, x2), x0, x(0, x2)), A__ISNAT(x(0, x2))) A__U51(tt, x0, x(plus(z0, z1), x2)) -> c12(A__U52(a__U31(a__U11(a__isNat(z0), z1), x2), x0, x(plus(z0, z1), x2)), A__ISNAT(x(plus(z0, z1), x2))) A__U51(tt, x0, x(s(z0), x2)) -> c12(A__U52(a__U31(a__U21(a__isNat(z0)), x2), x0, x(s(z0), x2)), A__ISNAT(x(s(z0), x2))) A__U51(tt, x0, x(x(z0, z1), x2)) -> c12(A__U52(a__U31(a__U31(a__isNat(z0), z1), x2), x0, x(x(z0, z1), x2)), A__ISNAT(x(x(z0, z1), x2))) A__U51(tt, x0, x(z0, x2)) -> c12(A__U52(a__U31(isNat(z0), x2), x0, x(z0, x2)), A__ISNAT(x(z0, x2))) A__U51(tt, x0, x(x1, z1)) -> c12(A__ISNAT(x(x1, z1))) A__U52(tt, U11(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U11(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U52(tt, U11(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U52(tt, U11(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U11(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U11(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U11(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U11(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U11(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U11(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U11(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U11(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U11(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U11(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U11(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U11(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U11(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U11(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U11(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U11(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U11(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U11(x0, x1), tt) -> c14(A__PLUS(tt, a__U11(mark(x0), x1))) A__U52(tt, U11(x0, x1), 0) -> c14(A__PLUS(0, a__U11(mark(x0), x1))) A__U52(tt, U12(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U12(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U52(tt, U12(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U12(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U12(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U12(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(tt), x1) -> c14(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U52(tt, U12(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U52(tt, U12(0), x1) -> c14(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U52(tt, U12(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U12(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U52(tt, U12(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U52(tt, U12(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U52(tt, U12(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U12(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U12(mark(x0))), MARK(U32(z0))) A__U52(tt, U12(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U12(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U12(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U12(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U12(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U12(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U12(mark(x0))), MARK(U61(z0))) A__U52(tt, U12(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U12(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U12(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U12(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U52(tt, U12(x0), x1) -> c14(MARK(x1)) A__U52(tt, U12(x0), tt) -> c14(A__PLUS(tt, a__U12(mark(x0)))) A__U52(tt, U12(x0), 0) -> c14(A__PLUS(0, a__U12(mark(x0)))) A__U52(tt, isNat(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U52(tt, isNat(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U31(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U52(tt, isNat(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U52(tt, isNat(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U52(tt, isNat(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U52(tt, isNat(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U52(tt, isNat(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__isNat(x0)), MARK(U32(z0))) A__U52(tt, isNat(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__isNat(x0)), MARK(U41(z0, z1))) A__U52(tt, isNat(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__isNat(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, isNat(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__isNat(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, isNat(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U52(tt, isNat(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__isNat(x0)), MARK(U61(z0))) A__U52(tt, isNat(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__isNat(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, isNat(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__isNat(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, isNat(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1))) A__U52(tt, isNat(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U52(tt, isNat(0), x1) -> c14(MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(MARK(x1)) A__U52(tt, isNat(x0), tt) -> c14(A__PLUS(tt, a__isNat(x0))) A__U52(tt, isNat(x0), 0) -> c14(A__PLUS(0, a__isNat(x0))) A__U52(tt, U21(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U21(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U52(tt, U21(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U21(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U21(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U21(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U21(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U21(tt), x1) -> c14(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U52(tt, U21(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U52(tt, U21(0), x1) -> c14(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U52(tt, U21(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U21(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U52(tt, U21(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U52(tt, U21(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U52(tt, U21(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U21(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U21(mark(x0))), MARK(U32(z0))) A__U52(tt, U21(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U21(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U21(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U21(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U21(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U21(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U21(mark(x0))), MARK(U61(z0))) A__U52(tt, U21(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U21(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U21(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U21(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U52(tt, U21(x0), x1) -> c14(MARK(x1)) A__U52(tt, U21(x0), tt) -> c14(A__PLUS(tt, a__U21(mark(x0)))) A__U52(tt, U21(x0), 0) -> c14(A__PLUS(0, a__U21(mark(x0)))) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, s(x1)) -> c12(A__ISNAT(s(x1))) A__U51(tt, x0, x(0, x2)) -> c12(A__U52(a__U31(tt, x2), x0, x(0, x2)), A__ISNAT(x(0, x2))) A__U51(tt, x0, x(plus(z0, z1), x2)) -> c12(A__U52(a__U31(a__U11(a__isNat(z0), z1), x2), x0, x(plus(z0, z1), x2)), A__ISNAT(x(plus(z0, z1), x2))) A__U51(tt, x0, x(s(z0), x2)) -> c12(A__U52(a__U31(a__U21(a__isNat(z0)), x2), x0, x(s(z0), x2)), A__ISNAT(x(s(z0), x2))) A__U51(tt, x0, x(x(z0, z1), x2)) -> c12(A__U52(a__U31(a__U31(a__isNat(z0), z1), x2), x0, x(x(z0, z1), x2)), A__ISNAT(x(x(z0, z1), x2))) A__U51(tt, x0, x(z0, x2)) -> c12(A__U52(a__U31(isNat(z0), x2), x0, x(z0, x2)), A__ISNAT(x(z0, x2))) A__U51(tt, x0, x(x1, z1)) -> c12(A__ISNAT(x(x1, z1))) A__U52(tt, U11(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U11(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U52(tt, U11(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U52(tt, U11(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U11(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U11(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U11(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U11(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U11(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U11(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U11(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U11(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U11(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U11(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U11(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U11(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U11(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U11(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U11(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U11(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U11(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U11(x0, x1), tt) -> c14(A__PLUS(tt, a__U11(mark(x0), x1))) A__U52(tt, U11(x0, x1), 0) -> c14(A__PLUS(0, a__U11(mark(x0), x1))) A__U52(tt, U12(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U12(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U52(tt, U12(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U12(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U12(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U12(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(tt), x1) -> c14(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U52(tt, U12(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U52(tt, U12(0), x1) -> c14(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U52(tt, U12(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U12(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U52(tt, U12(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U52(tt, U12(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U52(tt, U12(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U12(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U12(mark(x0))), MARK(U32(z0))) A__U52(tt, U12(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U12(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U12(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U12(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U12(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U12(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U12(mark(x0))), MARK(U61(z0))) A__U52(tt, U12(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U12(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U12(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U12(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U52(tt, U12(x0), x1) -> c14(MARK(x1)) A__U52(tt, U12(x0), tt) -> c14(A__PLUS(tt, a__U12(mark(x0)))) A__U52(tt, U12(x0), 0) -> c14(A__PLUS(0, a__U12(mark(x0)))) A__U52(tt, isNat(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U52(tt, isNat(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U31(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U52(tt, isNat(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U52(tt, isNat(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U52(tt, isNat(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U52(tt, isNat(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U52(tt, isNat(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__isNat(x0)), MARK(U32(z0))) A__U52(tt, isNat(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__isNat(x0)), MARK(U41(z0, z1))) A__U52(tt, isNat(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__isNat(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, isNat(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__isNat(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, isNat(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U52(tt, isNat(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__isNat(x0)), MARK(U61(z0))) A__U52(tt, isNat(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__isNat(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, isNat(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__isNat(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, isNat(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1))) A__U52(tt, isNat(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U52(tt, isNat(0), x1) -> c14(MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(MARK(x1)) A__U52(tt, isNat(x0), tt) -> c14(A__PLUS(tt, a__isNat(x0))) A__U52(tt, isNat(x0), 0) -> c14(A__PLUS(0, a__isNat(x0))) A__U52(tt, U21(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U21(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U52(tt, U21(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U21(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U21(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U21(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U21(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U21(tt), x1) -> c14(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U52(tt, U21(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U52(tt, U21(0), x1) -> c14(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U52(tt, U21(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U21(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U52(tt, U21(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U52(tt, U21(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U52(tt, U21(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U21(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U21(mark(x0))), MARK(U32(z0))) A__U52(tt, U21(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U21(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U21(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U21(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U21(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U21(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U21(mark(x0))), MARK(U61(z0))) A__U52(tt, U21(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U21(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U21(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U21(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U52(tt, U21(x0), x1) -> c14(MARK(x1)) A__U52(tt, U21(x0), tt) -> c14(A__PLUS(tt, a__U21(mark(x0)))) A__U52(tt, U21(x0), 0) -> c14(A__PLUS(0, a__U21(mark(x0)))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2, c43_1, c44_2, c44_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c49_2, c49_1, c50_2, c50_1, c51_2, c51_1, c12_2 ---------------------------------------- (203) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U52(tt, U31(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(x1)) by A__U52(tt, U31(x0, z1), x2) -> c14(A__PLUS(mark(x2), U31(mark(x0), z1)), MARK(x2)) A__U52(tt, U31(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U31(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U31(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U31(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U31(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U31(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U31(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U31(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U31(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U31(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U31(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U52(tt, U31(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U52(tt, U31(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U31(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U31(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U31(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U31(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U31(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U31(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U31(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U31(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U31(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U31(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U31(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U31(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U31(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U31(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U31(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U31(x0, x1), tt) -> c14(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(tt)) A__U52(tt, U31(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U31(x0, x1), 0) -> c14(A__PLUS(0, a__U31(mark(x0), x1)), MARK(0)) ---------------------------------------- (204) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, 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c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, s(x1)) -> c12(A__ISNAT(s(x1))) A__U51(tt, x0, x(0, x2)) -> c12(A__U52(a__U31(tt, x2), x0, x(0, x2)), A__ISNAT(x(0, x2))) A__U51(tt, x0, x(plus(z0, z1), x2)) -> c12(A__U52(a__U31(a__U11(a__isNat(z0), z1), x2), x0, x(plus(z0, z1), x2)), A__ISNAT(x(plus(z0, z1), x2))) A__U51(tt, x0, x(s(z0), x2)) -> c12(A__U52(a__U31(a__U21(a__isNat(z0)), x2), x0, x(s(z0), x2)), A__ISNAT(x(s(z0), x2))) A__U51(tt, x0, x(x(z0, z1), x2)) -> c12(A__U52(a__U31(a__U31(a__isNat(z0), z1), x2), x0, x(x(z0, z1), x2)), A__ISNAT(x(x(z0, z1), x2))) A__U51(tt, x0, x(z0, x2)) -> c12(A__U52(a__U31(isNat(z0), x2), x0, x(z0, x2)), A__ISNAT(x(z0, x2))) A__U51(tt, x0, x(x1, z1)) -> c12(A__ISNAT(x(x1, z1))) A__U52(tt, U11(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U11(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U52(tt, U11(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U52(tt, U11(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U11(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U11(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U11(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U11(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U11(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U11(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U11(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U11(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U11(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U11(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U11(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U11(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U11(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U11(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U11(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U11(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U11(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U11(x0, x1), tt) -> c14(A__PLUS(tt, a__U11(mark(x0), x1))) A__U52(tt, U11(x0, x1), 0) -> c14(A__PLUS(0, a__U11(mark(x0), x1))) A__U52(tt, U12(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U12(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U52(tt, U12(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U12(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U12(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U12(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(tt), x1) -> c14(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U52(tt, U12(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U52(tt, U12(0), x1) -> c14(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U52(tt, U12(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U12(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U52(tt, U12(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U52(tt, U12(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U52(tt, U12(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U12(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U12(mark(x0))), MARK(U32(z0))) A__U52(tt, U12(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U12(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U12(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U12(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U12(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U12(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U12(mark(x0))), MARK(U61(z0))) A__U52(tt, U12(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U12(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U12(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U12(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U52(tt, U12(x0), x1) -> c14(MARK(x1)) A__U52(tt, U12(x0), tt) -> c14(A__PLUS(tt, a__U12(mark(x0)))) A__U52(tt, U12(x0), 0) -> c14(A__PLUS(0, a__U12(mark(x0)))) A__U52(tt, isNat(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U52(tt, isNat(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U31(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U52(tt, isNat(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U52(tt, isNat(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U52(tt, isNat(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U52(tt, isNat(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U52(tt, isNat(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__isNat(x0)), MARK(U32(z0))) A__U52(tt, isNat(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__isNat(x0)), MARK(U41(z0, z1))) A__U52(tt, isNat(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__isNat(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, isNat(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__isNat(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, isNat(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U52(tt, isNat(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__isNat(x0)), MARK(U61(z0))) A__U52(tt, isNat(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__isNat(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, isNat(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__isNat(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, isNat(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1))) A__U52(tt, isNat(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U52(tt, isNat(0), x1) -> c14(MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(MARK(x1)) A__U52(tt, isNat(x0), tt) -> c14(A__PLUS(tt, a__isNat(x0))) A__U52(tt, isNat(x0), 0) -> c14(A__PLUS(0, a__isNat(x0))) A__U52(tt, U21(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U21(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U52(tt, U21(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U21(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U21(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U21(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U21(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U21(tt), x1) -> c14(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U52(tt, U21(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U52(tt, U21(0), x1) -> c14(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U52(tt, U21(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U21(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U52(tt, U21(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U52(tt, U21(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U52(tt, U21(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U21(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U21(mark(x0))), MARK(U32(z0))) A__U52(tt, U21(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U21(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U21(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U21(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U21(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U21(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U21(mark(x0))), MARK(U61(z0))) A__U52(tt, U21(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U21(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U21(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U21(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U52(tt, U21(x0), x1) -> c14(MARK(x1)) A__U52(tt, U21(x0), tt) -> c14(A__PLUS(tt, a__U21(mark(x0)))) A__U52(tt, U21(x0), 0) -> c14(A__PLUS(0, a__U21(mark(x0)))) A__U52(tt, U31(x0, z1), x2) -> c14(A__PLUS(mark(x2), U31(mark(x0), z1)), MARK(x2)) A__U52(tt, U31(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U31(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U31(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U31(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U31(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U31(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U31(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U31(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U31(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U31(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U31(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U52(tt, U31(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U52(tt, U31(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U31(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U31(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U31(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U31(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U31(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U31(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U31(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U31(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U31(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U31(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U31(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U31(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U31(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U31(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U31(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U31(x0, x1), tt) -> c14(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(tt)) A__U52(tt, U31(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U31(x0, x1), 0) -> c14(A__PLUS(0, a__U31(mark(x0), x1)), MARK(0)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> 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MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, s(x1)) -> c12(A__ISNAT(s(x1))) A__U51(tt, x0, x(0, x2)) -> c12(A__U52(a__U31(tt, x2), x0, x(0, x2)), A__ISNAT(x(0, x2))) A__U51(tt, x0, x(plus(z0, z1), x2)) -> c12(A__U52(a__U31(a__U11(a__isNat(z0), z1), x2), x0, x(plus(z0, z1), x2)), A__ISNAT(x(plus(z0, z1), x2))) A__U51(tt, x0, x(s(z0), x2)) -> c12(A__U52(a__U31(a__U21(a__isNat(z0)), x2), x0, x(s(z0), x2)), A__ISNAT(x(s(z0), x2))) A__U51(tt, x0, x(x(z0, z1), x2)) -> c12(A__U52(a__U31(a__U31(a__isNat(z0), z1), x2), x0, x(x(z0, z1), x2)), A__ISNAT(x(x(z0, z1), x2))) A__U51(tt, x0, x(z0, x2)) -> c12(A__U52(a__U31(isNat(z0), x2), x0, x(z0, x2)), A__ISNAT(x(z0, x2))) A__U51(tt, x0, x(x1, z1)) -> c12(A__ISNAT(x(x1, z1))) A__U52(tt, U11(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U11(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U52(tt, U11(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U52(tt, U11(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U11(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U11(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U11(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U11(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U11(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U11(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U11(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U11(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U11(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U11(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U11(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U11(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U11(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U11(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U11(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U11(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U11(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U11(x0, x1), tt) -> c14(A__PLUS(tt, a__U11(mark(x0), x1))) A__U52(tt, U11(x0, x1), 0) -> c14(A__PLUS(0, a__U11(mark(x0), x1))) A__U52(tt, U12(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U12(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U52(tt, U12(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U12(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U12(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U12(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(tt), x1) -> c14(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U52(tt, U12(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U52(tt, U12(0), x1) -> c14(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U52(tt, U12(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U12(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U52(tt, U12(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U52(tt, U12(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U52(tt, U12(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U12(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U12(mark(x0))), MARK(U32(z0))) A__U52(tt, U12(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U12(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U12(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U12(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U12(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U12(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U12(mark(x0))), MARK(U61(z0))) A__U52(tt, U12(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U12(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U12(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U12(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U52(tt, U12(x0), x1) -> c14(MARK(x1)) A__U52(tt, U12(x0), tt) -> c14(A__PLUS(tt, a__U12(mark(x0)))) A__U52(tt, U12(x0), 0) -> c14(A__PLUS(0, a__U12(mark(x0)))) A__U52(tt, isNat(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U52(tt, isNat(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U31(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U52(tt, isNat(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U52(tt, isNat(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U52(tt, isNat(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U52(tt, isNat(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U52(tt, isNat(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__isNat(x0)), MARK(U32(z0))) A__U52(tt, isNat(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__isNat(x0)), MARK(U41(z0, z1))) A__U52(tt, isNat(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__isNat(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, isNat(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__isNat(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, isNat(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U52(tt, isNat(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__isNat(x0)), MARK(U61(z0))) A__U52(tt, isNat(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__isNat(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, isNat(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__isNat(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, isNat(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1))) A__U52(tt, isNat(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U52(tt, isNat(0), x1) -> c14(MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(MARK(x1)) A__U52(tt, isNat(x0), tt) -> c14(A__PLUS(tt, a__isNat(x0))) A__U52(tt, isNat(x0), 0) -> c14(A__PLUS(0, a__isNat(x0))) A__U52(tt, U21(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U21(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U52(tt, U21(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U21(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U21(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U21(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U21(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U21(tt), x1) -> c14(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U52(tt, U21(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U52(tt, U21(0), x1) -> c14(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U52(tt, U21(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U21(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U52(tt, U21(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U52(tt, U21(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U52(tt, U21(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U21(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U21(mark(x0))), MARK(U32(z0))) A__U52(tt, U21(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U21(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U21(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U21(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U21(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U21(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U21(mark(x0))), MARK(U61(z0))) A__U52(tt, U21(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U21(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U21(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U21(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U52(tt, U21(x0), x1) -> c14(MARK(x1)) A__U52(tt, U21(x0), tt) -> c14(A__PLUS(tt, a__U21(mark(x0)))) A__U52(tt, U21(x0), 0) -> c14(A__PLUS(0, a__U21(mark(x0)))) A__U52(tt, U31(x0, z1), x2) -> c14(A__PLUS(mark(x2), U31(mark(x0), z1)), MARK(x2)) A__U52(tt, U31(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U31(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U31(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U31(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U31(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U31(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U31(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U31(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U31(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U31(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U31(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U52(tt, U31(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U52(tt, U31(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U31(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U31(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U31(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U31(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U31(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U31(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U31(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U31(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U31(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U31(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U31(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U31(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U31(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U31(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U31(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U31(x0, x1), tt) -> c14(A__PLUS(tt, a__U31(mark(x0), x1)), MARK(tt)) A__U52(tt, U31(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U31(x0, x1), 0) -> c14(A__PLUS(0, a__U31(mark(x0), x1)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2, c43_1, c44_2, c44_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c49_2, c49_1, c50_2, c50_1, c51_2, c51_1, c12_2 ---------------------------------------- (205) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (206) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), 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c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, 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c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, 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MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, s(x1)) -> c12(A__ISNAT(s(x1))) A__U51(tt, x0, x(0, x2)) -> c12(A__U52(a__U31(tt, x2), x0, x(0, x2)), A__ISNAT(x(0, x2))) A__U51(tt, x0, x(plus(z0, z1), x2)) -> c12(A__U52(a__U31(a__U11(a__isNat(z0), z1), x2), x0, x(plus(z0, z1), x2)), A__ISNAT(x(plus(z0, z1), x2))) A__U51(tt, x0, x(s(z0), x2)) -> c12(A__U52(a__U31(a__U21(a__isNat(z0)), x2), x0, x(s(z0), x2)), A__ISNAT(x(s(z0), x2))) A__U51(tt, x0, x(x(z0, z1), x2)) -> c12(A__U52(a__U31(a__U31(a__isNat(z0), z1), x2), x0, x(x(z0, z1), x2)), A__ISNAT(x(x(z0, z1), x2))) A__U51(tt, x0, x(z0, x2)) -> c12(A__U52(a__U31(isNat(z0), x2), x0, x(z0, x2)), A__ISNAT(x(z0, x2))) A__U51(tt, x0, x(x1, z1)) -> c12(A__ISNAT(x(x1, z1))) A__U52(tt, U11(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U11(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U52(tt, U11(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U52(tt, U11(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U11(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U11(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U11(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U11(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U11(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U11(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U11(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U11(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U11(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U11(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U11(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U11(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U11(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U11(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U11(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U11(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U11(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U11(x0, x1), tt) -> c14(A__PLUS(tt, a__U11(mark(x0), x1))) A__U52(tt, U11(x0, x1), 0) -> c14(A__PLUS(0, a__U11(mark(x0), x1))) A__U52(tt, U12(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U12(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U52(tt, U12(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U12(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U12(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U12(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(tt), x1) -> c14(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U52(tt, U12(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U52(tt, U12(0), x1) -> c14(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U52(tt, U12(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U12(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U52(tt, U12(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U52(tt, U12(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U52(tt, U12(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U12(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U12(mark(x0))), MARK(U32(z0))) A__U52(tt, U12(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U12(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U12(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U12(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U12(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U12(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U12(mark(x0))), MARK(U61(z0))) A__U52(tt, U12(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U12(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U12(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U12(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U52(tt, U12(x0), x1) -> c14(MARK(x1)) A__U52(tt, U12(x0), tt) -> c14(A__PLUS(tt, a__U12(mark(x0)))) A__U52(tt, U12(x0), 0) -> c14(A__PLUS(0, a__U12(mark(x0)))) A__U52(tt, isNat(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U52(tt, isNat(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U31(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U52(tt, isNat(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U52(tt, isNat(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U52(tt, isNat(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U52(tt, isNat(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U52(tt, isNat(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__isNat(x0)), MARK(U32(z0))) A__U52(tt, isNat(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__isNat(x0)), MARK(U41(z0, z1))) A__U52(tt, isNat(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__isNat(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, isNat(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__isNat(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, isNat(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U52(tt, isNat(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__isNat(x0)), MARK(U61(z0))) A__U52(tt, isNat(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__isNat(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, isNat(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__isNat(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, isNat(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1))) A__U52(tt, isNat(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U52(tt, isNat(0), x1) -> c14(MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(MARK(x1)) A__U52(tt, isNat(x0), tt) -> c14(A__PLUS(tt, a__isNat(x0))) A__U52(tt, isNat(x0), 0) -> c14(A__PLUS(0, a__isNat(x0))) A__U52(tt, U21(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U21(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U52(tt, U21(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U21(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U21(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U21(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U21(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U21(tt), x1) -> c14(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U52(tt, U21(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U52(tt, U21(0), x1) -> c14(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U52(tt, U21(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U21(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U52(tt, U21(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U52(tt, U21(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U52(tt, U21(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U21(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U21(mark(x0))), MARK(U32(z0))) A__U52(tt, U21(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U21(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U21(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U21(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U21(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U21(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U21(mark(x0))), MARK(U61(z0))) A__U52(tt, U21(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U21(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U21(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U21(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U52(tt, U21(x0), x1) -> c14(MARK(x1)) A__U52(tt, U21(x0), tt) -> c14(A__PLUS(tt, a__U21(mark(x0)))) A__U52(tt, U21(x0), 0) -> c14(A__PLUS(0, a__U21(mark(x0)))) A__U52(tt, U31(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U31(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U31(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U31(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U31(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U31(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U31(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U31(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U31(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U31(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U31(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U52(tt, U31(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U52(tt, U31(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U31(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U31(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U31(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U31(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U31(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U31(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U31(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U31(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U31(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U31(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U31(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U31(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U31(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U31(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U31(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U31(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U31(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U31(x0, x1), tt) -> c14(A__PLUS(tt, a__U31(mark(x0), x1))) A__U52(tt, U31(x0, x1), 0) -> c14(A__PLUS(0, a__U31(mark(x0), x1))) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> 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mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, s(x1)) -> c12(A__ISNAT(s(x1))) A__U51(tt, x0, x(0, x2)) -> c12(A__U52(a__U31(tt, x2), x0, x(0, x2)), A__ISNAT(x(0, x2))) A__U51(tt, x0, x(plus(z0, z1), x2)) -> c12(A__U52(a__U31(a__U11(a__isNat(z0), z1), x2), x0, x(plus(z0, z1), x2)), A__ISNAT(x(plus(z0, z1), x2))) A__U51(tt, x0, x(s(z0), x2)) -> c12(A__U52(a__U31(a__U21(a__isNat(z0)), x2), x0, x(s(z0), x2)), A__ISNAT(x(s(z0), x2))) A__U51(tt, x0, x(x(z0, z1), x2)) -> c12(A__U52(a__U31(a__U31(a__isNat(z0), z1), x2), x0, x(x(z0, z1), x2)), A__ISNAT(x(x(z0, z1), x2))) A__U51(tt, x0, x(z0, x2)) -> c12(A__U52(a__U31(isNat(z0), x2), x0, x(z0, x2)), A__ISNAT(x(z0, x2))) A__U51(tt, x0, x(x1, z1)) -> c12(A__ISNAT(x(x1, z1))) A__U52(tt, U11(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U11(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U52(tt, U11(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U52(tt, U11(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U11(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U11(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U11(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U11(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U11(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U11(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U11(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U11(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U11(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U11(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U11(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U11(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U11(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U11(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U11(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U11(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U11(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U11(x0, x1), tt) -> c14(A__PLUS(tt, a__U11(mark(x0), x1))) A__U52(tt, U11(x0, x1), 0) -> c14(A__PLUS(0, a__U11(mark(x0), x1))) A__U52(tt, U12(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U12(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U52(tt, U12(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U12(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U12(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U12(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(tt), x1) -> c14(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U52(tt, U12(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U52(tt, U12(0), x1) -> c14(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U52(tt, U12(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U12(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U52(tt, U12(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U52(tt, U12(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U52(tt, U12(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U12(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U12(mark(x0))), MARK(U32(z0))) A__U52(tt, U12(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U12(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U12(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U12(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U12(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U12(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U12(mark(x0))), MARK(U61(z0))) A__U52(tt, U12(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U12(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U12(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U12(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U52(tt, U12(x0), x1) -> c14(MARK(x1)) A__U52(tt, U12(x0), tt) -> c14(A__PLUS(tt, a__U12(mark(x0)))) A__U52(tt, U12(x0), 0) -> c14(A__PLUS(0, a__U12(mark(x0)))) A__U52(tt, isNat(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U52(tt, isNat(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U31(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U52(tt, isNat(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U52(tt, isNat(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U52(tt, isNat(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U52(tt, isNat(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U52(tt, isNat(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__isNat(x0)), MARK(U32(z0))) A__U52(tt, isNat(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__isNat(x0)), MARK(U41(z0, z1))) A__U52(tt, isNat(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__isNat(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, isNat(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__isNat(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, isNat(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U52(tt, isNat(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__isNat(x0)), MARK(U61(z0))) A__U52(tt, isNat(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__isNat(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, isNat(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__isNat(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, isNat(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1))) A__U52(tt, isNat(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U52(tt, isNat(0), x1) -> c14(MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(MARK(x1)) A__U52(tt, isNat(x0), tt) -> c14(A__PLUS(tt, a__isNat(x0))) A__U52(tt, isNat(x0), 0) -> c14(A__PLUS(0, a__isNat(x0))) A__U52(tt, U21(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U21(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U52(tt, U21(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U21(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U21(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U21(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U21(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U21(tt), x1) -> c14(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U52(tt, U21(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U52(tt, U21(0), x1) -> c14(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U52(tt, U21(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U21(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U52(tt, U21(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U52(tt, U21(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U52(tt, U21(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U21(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U21(mark(x0))), MARK(U32(z0))) A__U52(tt, U21(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U21(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U21(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U21(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U21(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U21(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U21(mark(x0))), MARK(U61(z0))) A__U52(tt, U21(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U21(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U21(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U21(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U52(tt, U21(x0), x1) -> c14(MARK(x1)) A__U52(tt, U21(x0), tt) -> c14(A__PLUS(tt, a__U21(mark(x0)))) A__U52(tt, U21(x0), 0) -> c14(A__PLUS(0, a__U21(mark(x0)))) A__U52(tt, U31(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U31(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U31(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U31(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U31(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U31(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U31(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U31(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U31(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U31(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U31(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U52(tt, U31(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U52(tt, U31(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U31(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U31(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U31(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U31(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U31(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U31(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U31(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U31(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U31(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U31(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U31(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U31(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U31(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U31(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U31(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U31(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U31(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U31(x0, x1), tt) -> c14(A__PLUS(tt, a__U31(mark(x0), x1))) A__U52(tt, U31(x0, x1), 0) -> c14(A__PLUS(0, a__U31(mark(x0), x1))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2, c43_1, c44_2, c44_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c49_2, c49_1, c50_2, c50_1, c51_2, c51_1, c12_2 ---------------------------------------- (207) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U52(tt, U32(z0), x1) -> c14(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(x1)) by A__U52(tt, U32(x0), x1) -> c14(A__PLUS(mark(x1), U32(mark(x0))), MARK(x1)) A__U52(tt, U32(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U32(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U32(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__isNat(z0))), MARK(x1)) A__U52(tt, U32(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U32(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U32(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U32(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U32(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U32(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U32(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U32(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U32(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U32(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U32(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U32(tt), x1) -> c14(A__PLUS(mark(x1), a__U32(tt)), MARK(x1)) A__U52(tt, U32(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U32(s(mark(z0)))), MARK(x1)) A__U52(tt, U32(0), x1) -> c14(A__PLUS(mark(x1), a__U32(0)), MARK(x1)) A__U52(tt, U32(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U32(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U32(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U32(mark(x0))), MARK(U12(z0))) A__U52(tt, U32(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U32(mark(x0))), MARK(isNat(z0))) A__U52(tt, U32(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U32(mark(x0))), MARK(U21(z0))) A__U52(tt, U32(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U32(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U32(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U32(mark(x0))), MARK(U32(z0))) A__U52(tt, U32(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U32(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U32(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U32(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U32(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U32(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U32(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U32(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U32(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U32(mark(x0))), MARK(U61(z0))) A__U52(tt, U32(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U32(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U32(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U32(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U32(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U32(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U32(x0), tt) -> c14(A__PLUS(tt, a__U32(mark(x0))), MARK(tt)) A__U52(tt, U32(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U32(mark(x0))), MARK(s(z0))) A__U52(tt, U32(x0), 0) -> c14(A__PLUS(0, a__U32(mark(x0))), MARK(0)) ---------------------------------------- (208) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, s(x1)) -> c12(A__ISNAT(s(x1))) A__U51(tt, x0, x(0, x2)) -> c12(A__U52(a__U31(tt, x2), x0, x(0, x2)), A__ISNAT(x(0, x2))) A__U51(tt, x0, x(plus(z0, z1), x2)) -> c12(A__U52(a__U31(a__U11(a__isNat(z0), z1), x2), x0, x(plus(z0, z1), x2)), A__ISNAT(x(plus(z0, z1), x2))) A__U51(tt, x0, x(s(z0), x2)) -> c12(A__U52(a__U31(a__U21(a__isNat(z0)), x2), x0, x(s(z0), x2)), A__ISNAT(x(s(z0), x2))) A__U51(tt, x0, x(x(z0, z1), x2)) -> c12(A__U52(a__U31(a__U31(a__isNat(z0), z1), x2), x0, x(x(z0, z1), x2)), A__ISNAT(x(x(z0, z1), x2))) A__U51(tt, x0, x(z0, x2)) -> c12(A__U52(a__U31(isNat(z0), x2), x0, x(z0, x2)), A__ISNAT(x(z0, x2))) A__U51(tt, x0, x(x1, z1)) -> c12(A__ISNAT(x(x1, z1))) A__U52(tt, U11(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U11(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U52(tt, U11(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U52(tt, U11(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U11(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U11(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U11(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U11(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U11(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U11(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U11(x0, x1), U41(z0, 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c14(A__PLUS(a__U61(mark(z0)), a__isNat(x0)), MARK(U61(z0))) A__U52(tt, isNat(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__isNat(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, isNat(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__isNat(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, isNat(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1))) A__U52(tt, isNat(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U52(tt, isNat(0), x1) -> c14(MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(MARK(x1)) A__U52(tt, isNat(x0), tt) -> c14(A__PLUS(tt, a__isNat(x0))) A__U52(tt, isNat(x0), 0) -> c14(A__PLUS(0, a__isNat(x0))) A__U52(tt, U21(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U21(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U52(tt, U21(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U21(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U21(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U21(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U21(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U21(tt), x1) -> c14(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U52(tt, U21(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U52(tt, U21(0), x1) -> c14(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U52(tt, U21(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U21(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U52(tt, U21(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U52(tt, U21(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U52(tt, U21(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U21(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U21(mark(x0))), MARK(U32(z0))) A__U52(tt, U21(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U21(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U21(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U21(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U21(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U21(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U21(mark(x0))), MARK(U61(z0))) A__U52(tt, U21(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U21(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U21(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U21(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U52(tt, U21(x0), x1) -> c14(MARK(x1)) A__U52(tt, U21(x0), tt) -> c14(A__PLUS(tt, a__U21(mark(x0)))) A__U52(tt, U21(x0), 0) -> c14(A__PLUS(0, a__U21(mark(x0)))) A__U52(tt, U31(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U31(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U31(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U31(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U31(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U31(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U31(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U31(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U31(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U31(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U31(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U52(tt, U31(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U52(tt, U31(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U31(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U31(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U31(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U31(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U31(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U31(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U31(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U31(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U31(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U31(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U31(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U31(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U31(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U31(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U31(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U31(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U31(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U31(x0, x1), tt) -> c14(A__PLUS(tt, a__U31(mark(x0), x1))) A__U52(tt, U31(x0, x1), 0) -> c14(A__PLUS(0, a__U31(mark(x0), x1))) A__U52(tt, U32(x0), x1) -> c14(A__PLUS(mark(x1), U32(mark(x0))), MARK(x1)) A__U52(tt, U32(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U32(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U32(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__isNat(z0))), MARK(x1)) A__U52(tt, U32(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U32(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U32(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U32(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U32(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U32(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U32(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U32(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U32(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U32(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U32(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U32(tt), x1) -> c14(A__PLUS(mark(x1), a__U32(tt)), MARK(x1)) A__U52(tt, U32(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U32(s(mark(z0)))), MARK(x1)) A__U52(tt, U32(0), x1) -> c14(A__PLUS(mark(x1), a__U32(0)), MARK(x1)) A__U52(tt, U32(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U32(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U32(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U32(mark(x0))), MARK(U12(z0))) A__U52(tt, U32(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U32(mark(x0))), MARK(isNat(z0))) A__U52(tt, U32(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U32(mark(x0))), MARK(U21(z0))) A__U52(tt, U32(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U32(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U32(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U32(mark(x0))), MARK(U32(z0))) A__U52(tt, U32(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U32(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U32(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U32(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U32(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U32(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U32(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U32(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U32(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U32(mark(x0))), MARK(U61(z0))) A__U52(tt, U32(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U32(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U32(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U32(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U32(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U32(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U32(x0), tt) -> c14(A__PLUS(tt, a__U32(mark(x0))), MARK(tt)) A__U52(tt, U32(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U32(mark(x0))), MARK(s(z0))) A__U52(tt, U32(x0), 0) -> c14(A__PLUS(0, a__U32(mark(x0))), MARK(0)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> 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MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, s(x1)) -> c12(A__ISNAT(s(x1))) A__U51(tt, x0, x(0, x2)) -> c12(A__U52(a__U31(tt, x2), x0, x(0, x2)), A__ISNAT(x(0, x2))) A__U51(tt, x0, x(plus(z0, z1), x2)) -> c12(A__U52(a__U31(a__U11(a__isNat(z0), z1), x2), x0, x(plus(z0, z1), x2)), A__ISNAT(x(plus(z0, z1), x2))) A__U51(tt, x0, x(s(z0), x2)) -> c12(A__U52(a__U31(a__U21(a__isNat(z0)), x2), x0, x(s(z0), x2)), A__ISNAT(x(s(z0), x2))) A__U51(tt, x0, x(x(z0, z1), x2)) -> c12(A__U52(a__U31(a__U31(a__isNat(z0), z1), x2), x0, x(x(z0, z1), x2)), A__ISNAT(x(x(z0, z1), x2))) A__U51(tt, x0, x(z0, x2)) -> c12(A__U52(a__U31(isNat(z0), x2), x0, x(z0, x2)), A__ISNAT(x(z0, x2))) A__U51(tt, x0, x(x1, z1)) -> c12(A__ISNAT(x(x1, z1))) A__U52(tt, U11(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U11(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U52(tt, U11(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U52(tt, U11(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U11(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U11(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U11(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U11(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U11(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U11(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U11(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U11(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U11(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U11(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U11(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U11(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U11(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U11(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U11(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U11(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U11(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U11(x0, x1), tt) -> c14(A__PLUS(tt, a__U11(mark(x0), x1))) A__U52(tt, U11(x0, x1), 0) -> c14(A__PLUS(0, a__U11(mark(x0), x1))) A__U52(tt, U12(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U12(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U52(tt, U12(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U12(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U12(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U12(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(tt), x1) -> c14(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U52(tt, U12(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U52(tt, U12(0), x1) -> c14(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U52(tt, U12(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U12(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U52(tt, U12(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U52(tt, U12(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U52(tt, U12(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U12(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U12(mark(x0))), MARK(U32(z0))) A__U52(tt, U12(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U12(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U12(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U12(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U12(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U12(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U12(mark(x0))), MARK(U61(z0))) A__U52(tt, U12(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U12(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U12(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U12(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U52(tt, U12(x0), x1) -> c14(MARK(x1)) A__U52(tt, U12(x0), tt) -> c14(A__PLUS(tt, a__U12(mark(x0)))) A__U52(tt, U12(x0), 0) -> c14(A__PLUS(0, a__U12(mark(x0)))) A__U52(tt, isNat(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) 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A__U52(tt, U32(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U32(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U32(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__isNat(z0))), MARK(x1)) A__U52(tt, U32(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U32(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U32(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U32(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U32(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U32(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U32(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U32(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U32(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U32(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U32(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U32(tt), x1) -> c14(A__PLUS(mark(x1), a__U32(tt)), MARK(x1)) A__U52(tt, U32(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U32(s(mark(z0)))), MARK(x1)) A__U52(tt, U32(0), x1) -> c14(A__PLUS(mark(x1), a__U32(0)), MARK(x1)) A__U52(tt, U32(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U32(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U32(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U32(mark(x0))), MARK(U12(z0))) A__U52(tt, U32(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U32(mark(x0))), MARK(isNat(z0))) A__U52(tt, U32(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U32(mark(x0))), MARK(U21(z0))) A__U52(tt, U32(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U32(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U32(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U32(mark(x0))), MARK(U32(z0))) A__U52(tt, U32(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U32(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U32(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U32(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U32(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U32(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U32(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U32(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U32(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U32(mark(x0))), MARK(U61(z0))) A__U52(tt, U32(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U32(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U32(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U32(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U32(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U32(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U32(x0), tt) -> c14(A__PLUS(tt, a__U32(mark(x0))), MARK(tt)) A__U52(tt, U32(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U32(mark(x0))), MARK(s(z0))) A__U52(tt, U32(x0), 0) -> c14(A__PLUS(0, a__U32(mark(x0))), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2, c43_1, c44_2, c44_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c49_2, c49_1, c50_2, c50_1, c51_2, c51_1, c12_2 ---------------------------------------- (209) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (210) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), 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c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, s(x1)) -> c12(A__ISNAT(s(x1))) A__U51(tt, x0, x(0, x2)) -> c12(A__U52(a__U31(tt, x2), x0, x(0, x2)), A__ISNAT(x(0, x2))) A__U51(tt, x0, x(plus(z0, z1), x2)) -> c12(A__U52(a__U31(a__U11(a__isNat(z0), z1), x2), x0, x(plus(z0, z1), x2)), A__ISNAT(x(plus(z0, z1), x2))) A__U51(tt, x0, x(s(z0), x2)) -> c12(A__U52(a__U31(a__U21(a__isNat(z0)), x2), x0, x(s(z0), x2)), A__ISNAT(x(s(z0), x2))) A__U51(tt, x0, x(x(z0, z1), x2)) -> c12(A__U52(a__U31(a__U31(a__isNat(z0), z1), x2), x0, x(x(z0, z1), x2)), A__ISNAT(x(x(z0, z1), x2))) A__U51(tt, x0, x(z0, x2)) -> c12(A__U52(a__U31(isNat(z0), x2), x0, x(z0, x2)), A__ISNAT(x(z0, x2))) A__U51(tt, x0, x(x1, z1)) -> c12(A__ISNAT(x(x1, z1))) A__U52(tt, U11(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U11(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U52(tt, U11(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U52(tt, U11(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U11(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U11(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U11(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U11(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U11(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U11(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U11(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U11(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U11(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U11(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U11(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U11(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U11(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U11(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U11(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U11(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U11(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U11(x0, x1), tt) -> c14(A__PLUS(tt, a__U11(mark(x0), x1))) A__U52(tt, U11(x0, x1), 0) -> c14(A__PLUS(0, a__U11(mark(x0), x1))) A__U52(tt, U12(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U12(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U52(tt, U12(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U12(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U12(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U12(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(tt), x1) -> c14(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U52(tt, U12(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U52(tt, U12(0), x1) -> c14(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U52(tt, U12(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U12(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U52(tt, U12(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U52(tt, U12(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U52(tt, U12(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U12(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U12(mark(x0))), MARK(U32(z0))) A__U52(tt, U12(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U12(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U12(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U12(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U12(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U12(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U12(mark(x0))), MARK(U61(z0))) A__U52(tt, U12(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U12(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U12(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U12(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U52(tt, U12(x0), x1) -> c14(MARK(x1)) A__U52(tt, U12(x0), tt) -> c14(A__PLUS(tt, a__U12(mark(x0)))) A__U52(tt, U12(x0), 0) -> c14(A__PLUS(0, a__U12(mark(x0)))) A__U52(tt, isNat(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U52(tt, isNat(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U31(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U52(tt, isNat(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U52(tt, isNat(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U52(tt, isNat(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U52(tt, isNat(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U52(tt, isNat(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__isNat(x0)), MARK(U32(z0))) A__U52(tt, isNat(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__isNat(x0)), MARK(U41(z0, z1))) A__U52(tt, isNat(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__isNat(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, isNat(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__isNat(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, isNat(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U52(tt, isNat(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__isNat(x0)), MARK(U61(z0))) A__U52(tt, isNat(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__isNat(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, isNat(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__isNat(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, isNat(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1))) A__U52(tt, isNat(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U52(tt, isNat(0), x1) -> c14(MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(MARK(x1)) A__U52(tt, isNat(x0), tt) -> c14(A__PLUS(tt, a__isNat(x0))) A__U52(tt, isNat(x0), 0) -> c14(A__PLUS(0, a__isNat(x0))) A__U52(tt, U21(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U21(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U52(tt, U21(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U21(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U21(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U21(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U21(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U21(tt), x1) -> c14(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U52(tt, U21(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U52(tt, U21(0), x1) -> c14(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U52(tt, U21(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U21(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U52(tt, U21(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U52(tt, U21(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U52(tt, U21(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U21(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U21(mark(x0))), MARK(U32(z0))) A__U52(tt, U21(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U21(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U21(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U21(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U21(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U21(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U21(mark(x0))), MARK(U61(z0))) A__U52(tt, U21(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U21(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U21(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U21(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U52(tt, U21(x0), x1) -> c14(MARK(x1)) A__U52(tt, U21(x0), tt) -> c14(A__PLUS(tt, a__U21(mark(x0)))) A__U52(tt, U21(x0), 0) -> c14(A__PLUS(0, a__U21(mark(x0)))) A__U52(tt, U31(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U31(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U31(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U31(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U31(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U31(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U31(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U31(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U31(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U31(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U31(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U52(tt, U31(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U52(tt, U31(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U31(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U31(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U31(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U31(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U31(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U31(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U31(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U31(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U31(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U31(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U31(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U31(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U31(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U31(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U31(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U31(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U31(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U31(x0, x1), tt) -> c14(A__PLUS(tt, a__U31(mark(x0), x1))) A__U52(tt, U31(x0, x1), 0) -> c14(A__PLUS(0, a__U31(mark(x0), x1))) A__U52(tt, U32(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U32(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U32(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__isNat(z0))), MARK(x1)) A__U52(tt, U32(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U32(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U32(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U32(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U32(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U32(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U32(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U32(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U32(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U32(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U32(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U32(tt), x1) -> c14(A__PLUS(mark(x1), a__U32(tt)), MARK(x1)) A__U52(tt, U32(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U32(s(mark(z0)))), MARK(x1)) A__U52(tt, U32(0), x1) -> c14(A__PLUS(mark(x1), a__U32(0)), MARK(x1)) A__U52(tt, U32(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U32(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U32(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U32(mark(x0))), MARK(U12(z0))) A__U52(tt, U32(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U32(mark(x0))), MARK(isNat(z0))) A__U52(tt, U32(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U32(mark(x0))), MARK(U21(z0))) A__U52(tt, U32(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U32(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U32(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U32(mark(x0))), MARK(U32(z0))) A__U52(tt, U32(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U32(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U32(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U32(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U32(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U32(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U32(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U32(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U32(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U32(mark(x0))), MARK(U61(z0))) A__U52(tt, U32(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U32(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U32(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U32(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U32(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U32(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U32(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U32(mark(x0))), MARK(s(z0))) A__U52(tt, U32(x0), x1) -> c14(MARK(x1)) A__U52(tt, U32(x0), tt) -> c14(A__PLUS(tt, a__U32(mark(x0)))) A__U52(tt, U32(x0), 0) -> c14(A__PLUS(0, a__U32(mark(x0)))) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, s(x1)) -> c12(A__ISNAT(s(x1))) A__U51(tt, x0, x(0, x2)) -> c12(A__U52(a__U31(tt, x2), x0, x(0, x2)), A__ISNAT(x(0, x2))) A__U51(tt, x0, x(plus(z0, z1), x2)) -> c12(A__U52(a__U31(a__U11(a__isNat(z0), z1), x2), x0, x(plus(z0, z1), x2)), A__ISNAT(x(plus(z0, z1), x2))) A__U51(tt, x0, x(s(z0), x2)) -> c12(A__U52(a__U31(a__U21(a__isNat(z0)), x2), x0, x(s(z0), x2)), A__ISNAT(x(s(z0), x2))) A__U51(tt, x0, x(x(z0, z1), x2)) -> c12(A__U52(a__U31(a__U31(a__isNat(z0), z1), x2), x0, x(x(z0, z1), x2)), A__ISNAT(x(x(z0, z1), x2))) A__U51(tt, x0, x(z0, x2)) -> c12(A__U52(a__U31(isNat(z0), x2), x0, x(z0, x2)), A__ISNAT(x(z0, x2))) A__U51(tt, x0, x(x1, z1)) -> c12(A__ISNAT(x(x1, z1))) A__U52(tt, U11(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U11(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U52(tt, U11(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U52(tt, U11(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U11(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U11(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U11(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U11(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U11(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U11(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U11(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U11(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U11(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U11(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U11(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U11(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U11(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U11(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U11(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U11(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U11(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U11(x0, x1), tt) -> c14(A__PLUS(tt, a__U11(mark(x0), x1))) A__U52(tt, U11(x0, x1), 0) -> c14(A__PLUS(0, a__U11(mark(x0), x1))) A__U52(tt, U12(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U12(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U52(tt, U12(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U12(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U12(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U12(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(tt), x1) -> c14(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U52(tt, U12(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U52(tt, U12(0), x1) -> c14(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U52(tt, U12(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U12(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U52(tt, U12(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U52(tt, U12(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U52(tt, U12(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U12(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U12(mark(x0))), MARK(U32(z0))) A__U52(tt, U12(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U12(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U12(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U12(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U12(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U12(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U12(mark(x0))), MARK(U61(z0))) A__U52(tt, U12(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U12(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U12(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U12(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U52(tt, U12(x0), x1) -> c14(MARK(x1)) A__U52(tt, U12(x0), tt) -> c14(A__PLUS(tt, a__U12(mark(x0)))) A__U52(tt, U12(x0), 0) -> c14(A__PLUS(0, a__U12(mark(x0)))) A__U52(tt, isNat(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U52(tt, isNat(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U31(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U52(tt, isNat(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U52(tt, isNat(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U52(tt, isNat(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U52(tt, isNat(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U52(tt, isNat(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__isNat(x0)), MARK(U32(z0))) A__U52(tt, isNat(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__isNat(x0)), MARK(U41(z0, z1))) A__U52(tt, isNat(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__isNat(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, isNat(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__isNat(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, isNat(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U52(tt, isNat(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__isNat(x0)), MARK(U61(z0))) A__U52(tt, isNat(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__isNat(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, isNat(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__isNat(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, isNat(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1))) A__U52(tt, isNat(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U52(tt, isNat(0), x1) -> c14(MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(MARK(x1)) A__U52(tt, isNat(x0), tt) -> c14(A__PLUS(tt, a__isNat(x0))) A__U52(tt, isNat(x0), 0) -> c14(A__PLUS(0, a__isNat(x0))) A__U52(tt, U21(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U21(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U52(tt, U21(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U21(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U21(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U21(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U21(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U21(tt), x1) -> c14(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U52(tt, U21(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U52(tt, U21(0), x1) -> c14(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U52(tt, U21(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U21(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U52(tt, U21(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U52(tt, U21(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U52(tt, U21(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U21(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U21(mark(x0))), MARK(U32(z0))) A__U52(tt, U21(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U21(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U21(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U21(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U21(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U21(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U21(mark(x0))), MARK(U61(z0))) A__U52(tt, U21(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U21(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U21(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U21(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U52(tt, U21(x0), x1) -> c14(MARK(x1)) A__U52(tt, U21(x0), tt) -> c14(A__PLUS(tt, a__U21(mark(x0)))) A__U52(tt, U21(x0), 0) -> c14(A__PLUS(0, a__U21(mark(x0)))) A__U52(tt, U31(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U31(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U31(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U31(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U31(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U31(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U31(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U31(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U31(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U31(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U31(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U52(tt, U31(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U52(tt, U31(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U31(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U31(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U31(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U31(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U31(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U31(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U31(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U31(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U31(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U31(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U31(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U31(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U31(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U31(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U31(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U31(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U31(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U31(x0, x1), tt) -> c14(A__PLUS(tt, a__U31(mark(x0), x1))) A__U52(tt, U31(x0, x1), 0) -> c14(A__PLUS(0, a__U31(mark(x0), x1))) A__U52(tt, U32(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U32(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U32(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__isNat(z0))), MARK(x1)) A__U52(tt, U32(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U32(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U32(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U32(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U32(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U32(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U32(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U32(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U32(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U32(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U32(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U32(tt), x1) -> c14(A__PLUS(mark(x1), a__U32(tt)), MARK(x1)) A__U52(tt, U32(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U32(s(mark(z0)))), MARK(x1)) A__U52(tt, U32(0), x1) -> c14(A__PLUS(mark(x1), a__U32(0)), MARK(x1)) A__U52(tt, U32(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U32(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U32(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U32(mark(x0))), MARK(U12(z0))) A__U52(tt, U32(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U32(mark(x0))), MARK(isNat(z0))) A__U52(tt, U32(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U32(mark(x0))), MARK(U21(z0))) A__U52(tt, U32(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U32(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U32(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U32(mark(x0))), MARK(U32(z0))) A__U52(tt, U32(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U32(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U32(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U32(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U32(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U32(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U32(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U32(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U32(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U32(mark(x0))), MARK(U61(z0))) A__U52(tt, U32(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U32(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U32(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U32(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U32(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U32(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U32(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U32(mark(x0))), MARK(s(z0))) A__U52(tt, U32(x0), x1) -> c14(MARK(x1)) A__U52(tt, U32(x0), tt) -> c14(A__PLUS(tt, a__U32(mark(x0)))) A__U52(tt, U32(x0), 0) -> c14(A__PLUS(0, a__U32(mark(x0)))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2, c43_1, c44_2, c44_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c49_2, c49_1, c50_2, c50_1, c51_2, c51_1, c12_2 ---------------------------------------- (211) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U52(tt, U41(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(x1)) by A__U52(tt, U41(x0, z1), x2) -> c14(A__PLUS(mark(x2), U41(mark(x0), z1)), MARK(x2)) A__U52(tt, U41(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U41(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U41(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U41(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U41(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U41(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U41(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U41(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U41(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U41(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U41(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U41(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U41(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U41(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U41(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U41(tt, x1)), MARK(x2)) A__U52(tt, U41(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U41(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U41(0, x1)), MARK(x2)) A__U52(tt, U41(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U41(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U41(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U41(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U41(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U41(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U41(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U41(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U41(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U41(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U41(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U41(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U41(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U41(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U41(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U41(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U41(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U41(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U41(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U41(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U41(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U41(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U41(x0, x1), tt) -> c14(A__PLUS(tt, a__U41(mark(x0), x1)), MARK(tt)) A__U52(tt, U41(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U41(x0, x1), 0) -> c14(A__PLUS(0, a__U41(mark(x0), x1)), MARK(0)) ---------------------------------------- (212) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, s(x1)) -> c12(A__ISNAT(s(x1))) A__U51(tt, x0, x(0, x2)) -> c12(A__U52(a__U31(tt, x2), x0, x(0, x2)), A__ISNAT(x(0, x2))) A__U51(tt, x0, x(plus(z0, z1), x2)) -> c12(A__U52(a__U31(a__U11(a__isNat(z0), z1), x2), x0, x(plus(z0, z1), x2)), A__ISNAT(x(plus(z0, z1), x2))) A__U51(tt, x0, x(s(z0), x2)) -> c12(A__U52(a__U31(a__U21(a__isNat(z0)), x2), x0, x(s(z0), x2)), A__ISNAT(x(s(z0), x2))) A__U51(tt, x0, x(x(z0, z1), x2)) -> c12(A__U52(a__U31(a__U31(a__isNat(z0), z1), x2), x0, x(x(z0, z1), x2)), A__ISNAT(x(x(z0, z1), x2))) A__U51(tt, x0, x(z0, x2)) -> c12(A__U52(a__U31(isNat(z0), x2), x0, x(z0, x2)), A__ISNAT(x(z0, x2))) A__U51(tt, x0, x(x1, z1)) -> c12(A__ISNAT(x(x1, z1))) A__U52(tt, U11(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U11(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U52(tt, U11(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U52(tt, U11(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U11(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U11(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U11(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U11(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U11(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U11(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U11(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U11(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U11(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U11(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U11(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U11(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U11(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U11(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U11(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U11(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U11(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U11(x0, x1), tt) -> c14(A__PLUS(tt, a__U11(mark(x0), x1))) A__U52(tt, U11(x0, x1), 0) -> c14(A__PLUS(0, a__U11(mark(x0), x1))) A__U52(tt, U12(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U12(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U52(tt, U12(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U12(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U12(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U12(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(tt), x1) -> c14(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U52(tt, U12(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U52(tt, U12(0), x1) -> c14(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U52(tt, U12(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U12(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U52(tt, U12(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U52(tt, U12(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U52(tt, U12(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U12(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U12(mark(x0))), MARK(U32(z0))) A__U52(tt, U12(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U12(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U12(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U12(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U12(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U12(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U12(mark(x0))), MARK(U61(z0))) A__U52(tt, U12(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U12(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U12(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U12(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U52(tt, U12(x0), x1) -> c14(MARK(x1)) A__U52(tt, U12(x0), tt) -> c14(A__PLUS(tt, a__U12(mark(x0)))) A__U52(tt, U12(x0), 0) -> c14(A__PLUS(0, a__U12(mark(x0)))) A__U52(tt, isNat(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U52(tt, isNat(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U31(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U52(tt, isNat(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U52(tt, isNat(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U52(tt, isNat(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U52(tt, isNat(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U52(tt, isNat(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__isNat(x0)), MARK(U32(z0))) A__U52(tt, isNat(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__isNat(x0)), MARK(U41(z0, z1))) A__U52(tt, isNat(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__isNat(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, isNat(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__isNat(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, isNat(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U52(tt, isNat(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__isNat(x0)), MARK(U61(z0))) A__U52(tt, isNat(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__isNat(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, isNat(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__isNat(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, isNat(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1))) A__U52(tt, isNat(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U52(tt, isNat(0), x1) -> c14(MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(MARK(x1)) A__U52(tt, isNat(x0), tt) -> c14(A__PLUS(tt, a__isNat(x0))) A__U52(tt, isNat(x0), 0) -> c14(A__PLUS(0, a__isNat(x0))) A__U52(tt, U21(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U21(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U52(tt, U21(U21(z0)), x1) -> 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a__U41(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U41(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U41(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U41(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U41(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U41(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U41(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U41(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U41(tt, x1)), MARK(x2)) A__U52(tt, U41(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U41(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U41(0, x1)), MARK(x2)) A__U52(tt, U41(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U41(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U41(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U41(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U41(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U41(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U41(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U41(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U41(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U41(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U41(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U41(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U41(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U41(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U41(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U41(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U41(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U41(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U41(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U41(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U41(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U41(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U41(x0, x1), tt) -> c14(A__PLUS(tt, a__U41(mark(x0), x1)), MARK(tt)) A__U52(tt, U41(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U41(x0, x1), 0) -> c14(A__PLUS(0, a__U41(mark(x0), x1)), MARK(0)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, 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c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, s(x1)) -> c12(A__ISNAT(s(x1))) A__U51(tt, x0, x(0, x2)) -> c12(A__U52(a__U31(tt, x2), x0, x(0, x2)), A__ISNAT(x(0, x2))) A__U51(tt, x0, x(plus(z0, z1), x2)) -> c12(A__U52(a__U31(a__U11(a__isNat(z0), z1), x2), x0, x(plus(z0, z1), x2)), A__ISNAT(x(plus(z0, z1), x2))) A__U51(tt, x0, x(s(z0), x2)) -> c12(A__U52(a__U31(a__U21(a__isNat(z0)), x2), x0, x(s(z0), x2)), A__ISNAT(x(s(z0), x2))) A__U51(tt, x0, x(x(z0, z1), x2)) -> c12(A__U52(a__U31(a__U31(a__isNat(z0), z1), x2), x0, x(x(z0, z1), x2)), A__ISNAT(x(x(z0, z1), x2))) A__U51(tt, x0, x(z0, x2)) -> c12(A__U52(a__U31(isNat(z0), x2), x0, x(z0, x2)), A__ISNAT(x(z0, x2))) A__U51(tt, x0, x(x1, z1)) -> c12(A__ISNAT(x(x1, z1))) A__U52(tt, U11(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U11(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U52(tt, U11(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U52(tt, U11(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U11(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U11(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U11(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U11(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U11(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U11(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U11(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U11(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U11(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U11(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U11(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U11(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U11(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U11(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U11(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U11(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U11(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U11(x0, x1), tt) -> c14(A__PLUS(tt, a__U11(mark(x0), x1))) A__U52(tt, U11(x0, x1), 0) -> c14(A__PLUS(0, a__U11(mark(x0), x1))) A__U52(tt, U12(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U12(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U52(tt, U12(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U12(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U12(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U12(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(tt), x1) -> c14(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U52(tt, U12(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U52(tt, U12(0), x1) -> c14(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U52(tt, U12(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U12(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U52(tt, U12(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U52(tt, U12(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U52(tt, U12(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U12(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U12(mark(x0))), MARK(U32(z0))) A__U52(tt, U12(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U12(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U12(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U12(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U12(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U12(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U12(mark(x0))), MARK(U61(z0))) A__U52(tt, U12(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U12(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U12(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U12(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U52(tt, U12(x0), x1) -> c14(MARK(x1)) A__U52(tt, U12(x0), tt) -> c14(A__PLUS(tt, a__U12(mark(x0)))) A__U52(tt, U12(x0), 0) -> c14(A__PLUS(0, a__U12(mark(x0)))) A__U52(tt, isNat(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U52(tt, isNat(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U31(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U52(tt, isNat(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U52(tt, isNat(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U52(tt, isNat(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U52(tt, isNat(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U52(tt, isNat(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__isNat(x0)), MARK(U32(z0))) A__U52(tt, isNat(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__isNat(x0)), MARK(U41(z0, z1))) A__U52(tt, isNat(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__isNat(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, isNat(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__isNat(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, isNat(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U52(tt, isNat(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__isNat(x0)), MARK(U61(z0))) A__U52(tt, isNat(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__isNat(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, isNat(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__isNat(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, isNat(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1))) A__U52(tt, isNat(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U52(tt, isNat(0), x1) -> c14(MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(MARK(x1)) A__U52(tt, isNat(x0), tt) -> c14(A__PLUS(tt, a__isNat(x0))) A__U52(tt, isNat(x0), 0) -> c14(A__PLUS(0, a__isNat(x0))) A__U52(tt, U21(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U21(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U52(tt, U21(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U21(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U21(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U21(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U21(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U21(tt), x1) -> c14(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U52(tt, U21(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U52(tt, U21(0), x1) -> c14(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U52(tt, U21(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U21(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U52(tt, U21(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U52(tt, U21(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U52(tt, U21(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U21(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U21(mark(x0))), MARK(U32(z0))) A__U52(tt, U21(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U21(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U21(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U21(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U21(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U21(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U21(mark(x0))), MARK(U61(z0))) A__U52(tt, U21(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U21(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U21(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U21(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U52(tt, U21(x0), x1) -> c14(MARK(x1)) A__U52(tt, U21(x0), tt) -> c14(A__PLUS(tt, a__U21(mark(x0)))) A__U52(tt, U21(x0), 0) -> c14(A__PLUS(0, a__U21(mark(x0)))) A__U52(tt, U31(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U31(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U31(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U31(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U31(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U31(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U31(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U31(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U31(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U31(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U31(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U52(tt, U31(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U52(tt, U31(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U31(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U31(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U31(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U31(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U31(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U31(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U31(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U31(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U31(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U31(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U31(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U31(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U31(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U31(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U31(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U31(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U31(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U31(x0, x1), tt) -> c14(A__PLUS(tt, a__U31(mark(x0), x1))) A__U52(tt, U31(x0, x1), 0) -> c14(A__PLUS(0, a__U31(mark(x0), x1))) A__U52(tt, U32(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U32(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U32(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__isNat(z0))), MARK(x1)) A__U52(tt, U32(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U32(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U32(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U32(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U32(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U32(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U32(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U32(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U32(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U32(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U32(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U32(tt), x1) -> c14(A__PLUS(mark(x1), a__U32(tt)), MARK(x1)) A__U52(tt, U32(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U32(s(mark(z0)))), MARK(x1)) A__U52(tt, U32(0), x1) -> c14(A__PLUS(mark(x1), a__U32(0)), MARK(x1)) A__U52(tt, U32(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U32(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U32(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U32(mark(x0))), MARK(U12(z0))) A__U52(tt, U32(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U32(mark(x0))), MARK(isNat(z0))) A__U52(tt, U32(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U32(mark(x0))), MARK(U21(z0))) A__U52(tt, U32(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U32(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U32(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U32(mark(x0))), MARK(U32(z0))) A__U52(tt, U32(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U32(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U32(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U32(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U32(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U32(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U32(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U32(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U32(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U32(mark(x0))), MARK(U61(z0))) A__U52(tt, U32(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U32(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U32(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U32(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U32(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U32(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U32(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U32(mark(x0))), MARK(s(z0))) A__U52(tt, U32(x0), x1) -> c14(MARK(x1)) A__U52(tt, U32(x0), tt) -> c14(A__PLUS(tt, a__U32(mark(x0)))) A__U52(tt, U32(x0), 0) -> c14(A__PLUS(0, a__U32(mark(x0)))) A__U52(tt, U41(x0, z1), x2) -> c14(A__PLUS(mark(x2), U41(mark(x0), z1)), MARK(x2)) A__U52(tt, U41(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U41(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U41(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U41(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U41(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U41(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U41(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U41(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U41(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U41(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U41(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U41(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U41(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U41(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U41(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U41(tt, x1)), MARK(x2)) A__U52(tt, U41(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U41(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U41(0, x1)), MARK(x2)) A__U52(tt, U41(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U41(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U41(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U41(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U41(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U41(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U41(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U41(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U41(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U41(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U41(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U41(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U41(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U41(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U41(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U41(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U41(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U41(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U41(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U41(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U41(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U41(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U41(x0, x1), tt) -> c14(A__PLUS(tt, a__U41(mark(x0), x1)), MARK(tt)) A__U52(tt, U41(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U41(x0, x1), 0) -> c14(A__PLUS(0, a__U41(mark(x0), x1)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2, c43_1, c44_2, c44_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c49_2, c49_1, c50_2, c50_1, c51_2, c51_1, c12_2 ---------------------------------------- (213) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (214) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, s(x1)) -> c12(A__ISNAT(s(x1))) A__U51(tt, x0, x(0, x2)) -> c12(A__U52(a__U31(tt, x2), x0, x(0, x2)), A__ISNAT(x(0, x2))) A__U51(tt, x0, x(plus(z0, z1), x2)) -> c12(A__U52(a__U31(a__U11(a__isNat(z0), z1), x2), x0, x(plus(z0, z1), x2)), A__ISNAT(x(plus(z0, z1), x2))) A__U51(tt, x0, x(s(z0), x2)) -> c12(A__U52(a__U31(a__U21(a__isNat(z0)), x2), x0, x(s(z0), x2)), A__ISNAT(x(s(z0), x2))) A__U51(tt, x0, x(x(z0, z1), x2)) -> c12(A__U52(a__U31(a__U31(a__isNat(z0), z1), x2), x0, x(x(z0, z1), x2)), A__ISNAT(x(x(z0, z1), x2))) A__U51(tt, x0, x(z0, x2)) -> c12(A__U52(a__U31(isNat(z0), x2), x0, x(z0, x2)), A__ISNAT(x(z0, x2))) A__U51(tt, x0, x(x1, z1)) -> c12(A__ISNAT(x(x1, z1))) A__U52(tt, U11(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U11(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U52(tt, U11(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U52(tt, U11(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U11(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U11(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U11(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U11(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U11(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U11(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U11(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U11(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U11(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U11(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U11(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U11(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U11(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U11(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U11(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U11(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U11(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U11(x0, x1), tt) -> c14(A__PLUS(tt, a__U11(mark(x0), x1))) A__U52(tt, U11(x0, x1), 0) -> c14(A__PLUS(0, a__U11(mark(x0), x1))) A__U52(tt, U12(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U12(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U52(tt, U12(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U12(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U12(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U12(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(tt), x1) -> c14(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U52(tt, U12(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U52(tt, U12(0), x1) -> c14(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U52(tt, U12(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U12(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U52(tt, U12(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U52(tt, U12(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U52(tt, U12(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U12(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U12(mark(x0))), MARK(U32(z0))) A__U52(tt, U12(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U12(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U12(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U12(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U12(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U12(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U12(mark(x0))), MARK(U61(z0))) A__U52(tt, U12(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U12(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U12(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U12(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U52(tt, U12(x0), x1) -> c14(MARK(x1)) A__U52(tt, U12(x0), tt) -> c14(A__PLUS(tt, a__U12(mark(x0)))) A__U52(tt, U12(x0), 0) -> c14(A__PLUS(0, a__U12(mark(x0)))) A__U52(tt, isNat(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U52(tt, isNat(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U31(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U52(tt, isNat(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U52(tt, isNat(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U52(tt, isNat(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U52(tt, isNat(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U52(tt, isNat(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__isNat(x0)), MARK(U32(z0))) A__U52(tt, isNat(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__isNat(x0)), MARK(U41(z0, z1))) 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A__U52(tt, U21(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U21(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U21(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U52(tt, U21(x0), x1) -> c14(MARK(x1)) A__U52(tt, U21(x0), tt) -> c14(A__PLUS(tt, a__U21(mark(x0)))) A__U52(tt, U21(x0), 0) -> c14(A__PLUS(0, a__U21(mark(x0)))) A__U52(tt, U31(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U31(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U31(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, 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MARK(x1)) A__U52(tt, U32(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U32(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U32(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U32(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U32(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U32(tt), x1) -> c14(A__PLUS(mark(x1), a__U32(tt)), MARK(x1)) A__U52(tt, U32(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U32(s(mark(z0)))), MARK(x1)) A__U52(tt, U32(0), x1) -> c14(A__PLUS(mark(x1), a__U32(0)), MARK(x1)) A__U52(tt, U32(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U32(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U32(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U32(mark(x0))), MARK(U12(z0))) A__U52(tt, U32(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U32(mark(x0))), MARK(isNat(z0))) A__U52(tt, U32(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U32(mark(x0))), MARK(U21(z0))) A__U52(tt, U32(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U32(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U32(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U32(mark(x0))), MARK(U32(z0))) A__U52(tt, U32(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U32(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U32(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U32(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U32(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U32(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U32(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U32(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U32(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U32(mark(x0))), MARK(U61(z0))) A__U52(tt, U32(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U32(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U32(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U32(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U32(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U32(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U32(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U32(mark(x0))), MARK(s(z0))) A__U52(tt, U32(x0), x1) -> c14(MARK(x1)) A__U52(tt, U32(x0), tt) -> c14(A__PLUS(tt, a__U32(mark(x0)))) A__U52(tt, U32(x0), 0) -> c14(A__PLUS(0, a__U32(mark(x0)))) A__U52(tt, U41(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U41(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U41(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U41(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U41(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U41(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U41(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U41(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U41(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U41(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U41(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U41(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U41(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U41(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U41(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U41(tt, x1)), MARK(x2)) A__U52(tt, U41(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U41(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U41(0, x1)), MARK(x2)) A__U52(tt, U41(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U41(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U41(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U41(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U41(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U41(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U41(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U41(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U41(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U41(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U41(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U41(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U41(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U41(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U41(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U41(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U41(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U41(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U41(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U41(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U41(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U41(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U41(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U41(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U41(x0, x1), tt) -> c14(A__PLUS(tt, a__U41(mark(x0), x1))) A__U52(tt, U41(x0, x1), 0) -> c14(A__PLUS(0, a__U41(mark(x0), x1))) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), 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c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, s(x1)) -> c12(A__ISNAT(s(x1))) A__U51(tt, x0, x(0, x2)) -> c12(A__U52(a__U31(tt, x2), x0, x(0, x2)), A__ISNAT(x(0, x2))) A__U51(tt, x0, x(plus(z0, z1), x2)) -> c12(A__U52(a__U31(a__U11(a__isNat(z0), z1), x2), x0, x(plus(z0, z1), x2)), A__ISNAT(x(plus(z0, z1), x2))) A__U51(tt, x0, x(s(z0), x2)) -> c12(A__U52(a__U31(a__U21(a__isNat(z0)), x2), x0, x(s(z0), x2)), A__ISNAT(x(s(z0), x2))) A__U51(tt, x0, x(x(z0, z1), x2)) -> c12(A__U52(a__U31(a__U31(a__isNat(z0), z1), x2), x0, x(x(z0, z1), x2)), A__ISNAT(x(x(z0, z1), x2))) A__U51(tt, x0, x(z0, x2)) -> c12(A__U52(a__U31(isNat(z0), x2), x0, x(z0, x2)), A__ISNAT(x(z0, x2))) A__U51(tt, x0, x(x1, z1)) -> c12(A__ISNAT(x(x1, z1))) A__U52(tt, U11(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U11(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U52(tt, U11(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U52(tt, U11(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U11(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U11(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U11(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U11(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U11(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U11(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U11(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U11(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U11(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U11(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U11(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U11(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U11(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U11(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U11(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U11(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U11(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U11(x0, x1), tt) -> c14(A__PLUS(tt, a__U11(mark(x0), x1))) A__U52(tt, U11(x0, x1), 0) -> c14(A__PLUS(0, a__U11(mark(x0), x1))) A__U52(tt, U12(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U12(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U52(tt, U12(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U12(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U12(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U12(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(tt), x1) -> c14(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U52(tt, U12(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U52(tt, U12(0), x1) -> c14(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U52(tt, U12(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U12(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U52(tt, U12(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U52(tt, U12(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U52(tt, U12(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U12(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U12(mark(x0))), MARK(U32(z0))) A__U52(tt, U12(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U12(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U12(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U12(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U12(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U12(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U12(mark(x0))), MARK(U61(z0))) A__U52(tt, U12(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U12(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U12(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U12(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U52(tt, U12(x0), x1) -> c14(MARK(x1)) A__U52(tt, U12(x0), tt) -> c14(A__PLUS(tt, a__U12(mark(x0)))) A__U52(tt, U12(x0), 0) -> c14(A__PLUS(0, a__U12(mark(x0)))) A__U52(tt, isNat(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U52(tt, isNat(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U31(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U52(tt, isNat(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U52(tt, isNat(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U52(tt, isNat(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U52(tt, isNat(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U52(tt, isNat(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__isNat(x0)), MARK(U32(z0))) A__U52(tt, isNat(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__isNat(x0)), MARK(U41(z0, z1))) A__U52(tt, isNat(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__isNat(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, isNat(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__isNat(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, isNat(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U52(tt, isNat(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__isNat(x0)), MARK(U61(z0))) A__U52(tt, isNat(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__isNat(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, isNat(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__isNat(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, isNat(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1))) A__U52(tt, isNat(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U52(tt, isNat(0), x1) -> c14(MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(MARK(x1)) A__U52(tt, isNat(x0), tt) -> c14(A__PLUS(tt, a__isNat(x0))) A__U52(tt, isNat(x0), 0) -> c14(A__PLUS(0, a__isNat(x0))) A__U52(tt, U21(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U21(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U52(tt, U21(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U21(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U21(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U21(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U21(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U21(tt), x1) -> c14(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U52(tt, U21(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U52(tt, U21(0), x1) -> c14(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U52(tt, U21(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U21(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U52(tt, U21(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U52(tt, U21(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U52(tt, U21(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U21(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U21(mark(x0))), MARK(U32(z0))) A__U52(tt, U21(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U21(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U21(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U21(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U21(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U21(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U21(mark(x0))), MARK(U61(z0))) A__U52(tt, U21(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U21(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U21(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U21(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U52(tt, U21(x0), x1) -> c14(MARK(x1)) A__U52(tt, U21(x0), tt) -> c14(A__PLUS(tt, a__U21(mark(x0)))) A__U52(tt, U21(x0), 0) -> c14(A__PLUS(0, a__U21(mark(x0)))) A__U52(tt, U31(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U31(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U31(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U31(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U31(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U31(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U31(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U31(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U31(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U31(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U31(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U31(tt, x1)), MARK(x2)) A__U52(tt, U31(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U31(0, x1)), MARK(x2)) A__U52(tt, U31(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U31(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U31(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U31(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U31(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U31(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U31(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U31(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U31(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U31(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U31(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U31(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U31(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U31(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U31(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U31(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U31(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U31(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U31(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U31(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U31(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U31(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U31(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U31(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U31(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U31(x0, x1), tt) -> c14(A__PLUS(tt, a__U31(mark(x0), x1))) A__U52(tt, U31(x0, x1), 0) -> c14(A__PLUS(0, a__U31(mark(x0), x1))) A__U52(tt, U32(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U32(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U32(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__isNat(z0))), MARK(x1)) A__U52(tt, U32(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U32(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U32(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U32(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U32(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U32(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U32(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U32(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U32(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U32(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U32(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U32(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U32(tt), x1) -> c14(A__PLUS(mark(x1), a__U32(tt)), MARK(x1)) A__U52(tt, U32(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U32(s(mark(z0)))), MARK(x1)) A__U52(tt, U32(0), x1) -> c14(A__PLUS(mark(x1), a__U32(0)), MARK(x1)) A__U52(tt, U32(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U32(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U32(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U32(mark(x0))), MARK(U12(z0))) A__U52(tt, U32(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U32(mark(x0))), MARK(isNat(z0))) A__U52(tt, U32(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U32(mark(x0))), MARK(U21(z0))) A__U52(tt, U32(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U32(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U32(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U32(mark(x0))), MARK(U32(z0))) A__U52(tt, U32(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U32(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U32(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U32(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U32(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U32(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U32(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U32(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U32(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U32(mark(x0))), MARK(U61(z0))) A__U52(tt, U32(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U32(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U32(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U32(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U32(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U32(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U32(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U32(mark(x0))), MARK(s(z0))) A__U52(tt, U32(x0), x1) -> c14(MARK(x1)) A__U52(tt, U32(x0), tt) -> c14(A__PLUS(tt, a__U32(mark(x0)))) A__U52(tt, U32(x0), 0) -> c14(A__PLUS(0, a__U32(mark(x0)))) A__U52(tt, U41(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U41(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U41(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U41(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U41(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U41(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U41(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U41(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U41(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U41(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U41(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U41(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U41(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U41(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U41(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U41(tt, x1)), MARK(x2)) A__U52(tt, U41(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U41(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U41(0, x1)), MARK(x2)) A__U52(tt, U41(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U41(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U41(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U41(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U41(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U41(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U41(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U41(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U41(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U41(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U41(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U41(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U41(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U41(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U41(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U41(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U41(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U41(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U41(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U41(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U41(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U41(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U41(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U41(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U41(x0, x1), tt) -> c14(A__PLUS(tt, a__U41(mark(x0), x1))) A__U52(tt, U41(x0, x1), 0) -> c14(A__PLUS(0, a__U41(mark(x0), x1))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2, c43_1, c44_2, c44_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c49_2, c49_1, c50_2, c50_1, c51_2, c51_1, c12_2 ---------------------------------------- (215) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U52(tt, U51(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(x1)) by A__U52(tt, U51(x0, z1, z2), x3) -> c14(A__PLUS(mark(x3), U51(mark(x0), z1, z2)), MARK(x3)) A__U52(tt, U51(U11(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U52(tt, U51(U12(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U51(isNat(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__isNat(z0), x1, x2)), MARK(x3)) A__U52(tt, U51(U21(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U51(U31(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U52(tt, U51(U32(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U32(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U51(U41(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U41(mark(z0), z1), x1, x2)), MARK(x3)) A__U52(tt, U51(U51(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U51(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U51(U52(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U52(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U51(plus(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U52(tt, U51(U61(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U61(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U51(U71(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U71(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U51(U72(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U72(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U51(x(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U52(tt, U51(tt, x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(tt, x1, x2)), MARK(x3)) A__U52(tt, U51(s(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(s(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U51(0, x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(0, x1, x2)), MARK(x3)) A__U52(tt, U51(x0, x1, x2), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U51(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U52(tt, U51(x0, x1, x2), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(U12(z0))) A__U52(tt, U51(x0, x1, x2), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U51(mark(x0), x1, x2)), MARK(isNat(z0))) A__U52(tt, U51(x0, x1, x2), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(U21(z0))) A__U52(tt, U51(x0, x1, x2), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U51(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U52(tt, U51(x0, x1, x2), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(U32(z0))) A__U52(tt, U51(x0, x1, x2), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U51(mark(x0), x1, x2)), MARK(U41(z0, z1))) A__U52(tt, U51(x0, x1, x2), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U51(mark(x0), x1, x2)), MARK(U51(z0, z1, z2))) A__U52(tt, U51(x0, x1, x2), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U51(mark(x0), x1, x2)), MARK(U52(z0, z1, z2))) A__U52(tt, U51(x0, x1, x2), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U51(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U52(tt, U51(x0, x1, x2), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(U61(z0))) A__U52(tt, U51(x0, x1, x2), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U51(mark(x0), x1, x2)), MARK(U71(z0, z1, z2))) A__U52(tt, U51(x0, x1, x2), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U51(mark(x0), x1, x2)), MARK(U72(z0, z1, z2))) A__U52(tt, U51(x0, x1, x2), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U51(mark(x0), x1, x2)), MARK(x(z0, z1))) A__U52(tt, U51(x0, x1, x2), tt) -> c14(A__PLUS(tt, a__U51(mark(x0), x1, x2)), MARK(tt)) A__U52(tt, U51(x0, x1, x2), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(s(z0))) A__U52(tt, U51(x0, x1, x2), 0) -> c14(A__PLUS(0, a__U51(mark(x0), x1, x2)), MARK(0)) ---------------------------------------- (216) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, s(x1)) -> c12(A__ISNAT(s(x1))) A__U51(tt, x0, x(0, x2)) -> c12(A__U52(a__U31(tt, x2), x0, x(0, x2)), A__ISNAT(x(0, x2))) A__U51(tt, x0, x(plus(z0, z1), x2)) -> c12(A__U52(a__U31(a__U11(a__isNat(z0), z1), x2), x0, x(plus(z0, z1), x2)), A__ISNAT(x(plus(z0, z1), x2))) A__U51(tt, x0, x(s(z0), x2)) -> c12(A__U52(a__U31(a__U21(a__isNat(z0)), x2), x0, x(s(z0), x2)), A__ISNAT(x(s(z0), x2))) A__U51(tt, x0, x(x(z0, z1), x2)) -> c12(A__U52(a__U31(a__U31(a__isNat(z0), z1), x2), x0, x(x(z0, z1), x2)), A__ISNAT(x(x(z0, z1), x2))) A__U51(tt, x0, x(z0, x2)) -> c12(A__U52(a__U31(isNat(z0), x2), x0, x(z0, x2)), A__ISNAT(x(z0, x2))) A__U51(tt, x0, x(x1, z1)) -> c12(A__ISNAT(x(x1, z1))) A__U52(tt, U11(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U11(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U52(tt, U11(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U52(tt, U11(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U11(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U11(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U11(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U11(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U11(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U11(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U11(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U11(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U11(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U11(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U11(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U11(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U11(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U11(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U11(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U11(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U11(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U11(x0, x1), tt) -> c14(A__PLUS(tt, a__U11(mark(x0), x1))) A__U52(tt, U11(x0, x1), 0) -> c14(A__PLUS(0, a__U11(mark(x0), x1))) A__U52(tt, U12(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U12(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U52(tt, U12(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U12(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U12(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U12(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(tt), x1) -> c14(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U52(tt, U12(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U52(tt, U12(0), x1) -> c14(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U52(tt, U12(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U12(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U52(tt, U12(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U52(tt, U12(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U52(tt, U12(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U12(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U12(mark(x0))), MARK(U32(z0))) A__U52(tt, U12(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U12(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U12(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U12(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U12(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U12(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U12(mark(x0))), MARK(U61(z0))) A__U52(tt, U12(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U12(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U12(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U12(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U52(tt, U12(x0), x1) -> c14(MARK(x1)) A__U52(tt, U12(x0), tt) -> c14(A__PLUS(tt, a__U12(mark(x0)))) A__U52(tt, U12(x0), 0) -> c14(A__PLUS(0, a__U12(mark(x0)))) A__U52(tt, isNat(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U52(tt, isNat(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U31(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U52(tt, isNat(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U52(tt, isNat(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U52(tt, isNat(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U52(tt, isNat(x0), U31(z0, z1)) -> 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z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U32(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U32(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U32(mark(x0))), MARK(U61(z0))) A__U52(tt, U32(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U32(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U32(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U32(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U32(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U32(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U32(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U32(mark(x0))), MARK(s(z0))) A__U52(tt, U32(x0), x1) -> c14(MARK(x1)) A__U52(tt, U32(x0), tt) -> c14(A__PLUS(tt, a__U32(mark(x0)))) A__U52(tt, U32(x0), 0) -> c14(A__PLUS(0, a__U32(mark(x0)))) A__U52(tt, U41(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U41(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, 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c14(A__PLUS(mark(x2), a__U41(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U41(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U41(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U41(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U41(tt, x1)), MARK(x2)) A__U52(tt, U41(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U41(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U41(0, x1)), MARK(x2)) A__U52(tt, U41(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U41(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U41(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U41(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U41(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U41(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U41(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U41(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U41(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U41(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U41(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U41(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U41(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U41(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U41(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U41(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U41(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U41(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U41(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U41(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U41(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U41(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U41(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U41(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U41(x0, x1), tt) -> c14(A__PLUS(tt, a__U41(mark(x0), x1))) A__U52(tt, U41(x0, x1), 0) -> c14(A__PLUS(0, a__U41(mark(x0), x1))) A__U52(tt, U51(x0, z1, z2), x3) -> c14(A__PLUS(mark(x3), U51(mark(x0), z1, z2)), MARK(x3)) A__U52(tt, U51(U11(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U52(tt, U51(U12(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U51(isNat(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__isNat(z0), x1, x2)), MARK(x3)) A__U52(tt, U51(U21(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U51(U31(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U52(tt, U51(U32(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U32(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U51(U41(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U41(mark(z0), z1), x1, x2)), MARK(x3)) A__U52(tt, U51(U51(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U51(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U51(U52(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U52(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U51(plus(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U52(tt, U51(U61(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U61(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U51(U71(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U71(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U51(U72(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U72(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U51(x(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U52(tt, U51(tt, x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(tt, x1, x2)), MARK(x3)) A__U52(tt, U51(s(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(s(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U51(0, x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(0, x1, x2)), MARK(x3)) A__U52(tt, U51(x0, x1, x2), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U51(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U52(tt, U51(x0, x1, x2), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(U12(z0))) A__U52(tt, U51(x0, x1, x2), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U51(mark(x0), x1, x2)), MARK(isNat(z0))) A__U52(tt, U51(x0, x1, x2), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(U21(z0))) A__U52(tt, U51(x0, x1, x2), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U51(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U52(tt, U51(x0, x1, x2), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(U32(z0))) A__U52(tt, U51(x0, x1, x2), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U51(mark(x0), x1, x2)), MARK(U41(z0, z1))) A__U52(tt, U51(x0, x1, x2), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U51(mark(x0), x1, x2)), MARK(U51(z0, z1, z2))) A__U52(tt, U51(x0, x1, x2), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U51(mark(x0), x1, x2)), MARK(U52(z0, z1, z2))) A__U52(tt, U51(x0, x1, x2), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U51(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U52(tt, U51(x0, x1, x2), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(U61(z0))) A__U52(tt, U51(x0, x1, x2), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U51(mark(x0), x1, x2)), MARK(U71(z0, z1, z2))) A__U52(tt, U51(x0, x1, x2), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U51(mark(x0), x1, x2)), MARK(U72(z0, z1, z2))) A__U52(tt, U51(x0, x1, x2), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U51(mark(x0), x1, x2)), MARK(x(z0, z1))) A__U52(tt, U51(x0, x1, x2), tt) -> c14(A__PLUS(tt, a__U51(mark(x0), x1, x2)), MARK(tt)) A__U52(tt, U51(x0, x1, x2), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(s(z0))) A__U52(tt, U51(x0, x1, x2), 0) -> c14(A__PLUS(0, a__U51(mark(x0), x1, x2)), MARK(0)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, s(x1)) -> c12(A__ISNAT(s(x1))) A__U51(tt, x0, x(0, x2)) -> c12(A__U52(a__U31(tt, x2), x0, x(0, x2)), A__ISNAT(x(0, x2))) A__U51(tt, x0, x(plus(z0, z1), x2)) -> c12(A__U52(a__U31(a__U11(a__isNat(z0), z1), x2), x0, x(plus(z0, z1), x2)), A__ISNAT(x(plus(z0, z1), x2))) A__U51(tt, x0, x(s(z0), x2)) -> c12(A__U52(a__U31(a__U21(a__isNat(z0)), x2), x0, x(s(z0), x2)), A__ISNAT(x(s(z0), x2))) A__U51(tt, x0, x(x(z0, z1), x2)) -> c12(A__U52(a__U31(a__U31(a__isNat(z0), z1), x2), x0, x(x(z0, z1), x2)), A__ISNAT(x(x(z0, z1), x2))) A__U51(tt, x0, x(z0, x2)) -> c12(A__U52(a__U31(isNat(z0), x2), x0, x(z0, x2)), A__ISNAT(x(z0, x2))) A__U51(tt, x0, x(x1, z1)) -> c12(A__ISNAT(x(x1, z1))) A__U52(tt, U11(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U11(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U52(tt, U11(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U52(tt, U11(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U11(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U11(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U11(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U11(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U11(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U11(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U11(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U11(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U11(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U11(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U11(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U11(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U11(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U11(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U11(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U11(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U11(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U11(x0, x1), tt) -> c14(A__PLUS(tt, a__U11(mark(x0), x1))) A__U52(tt, U11(x0, x1), 0) -> c14(A__PLUS(0, a__U11(mark(x0), x1))) A__U52(tt, U12(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U12(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U52(tt, U12(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U12(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U12(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U12(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(tt), x1) -> c14(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U52(tt, U12(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U52(tt, U12(0), x1) -> c14(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U52(tt, U12(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U12(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U52(tt, U12(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U52(tt, U12(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U52(tt, U12(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U12(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U12(mark(x0))), MARK(U32(z0))) A__U52(tt, U12(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U12(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U12(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U12(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U12(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U12(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U12(mark(x0))), MARK(U61(z0))) A__U52(tt, U12(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U12(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U12(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U12(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U52(tt, U12(x0), x1) -> c14(MARK(x1)) A__U52(tt, U12(x0), tt) -> c14(A__PLUS(tt, a__U12(mark(x0)))) A__U52(tt, U12(x0), 0) -> c14(A__PLUS(0, a__U12(mark(x0)))) A__U52(tt, isNat(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U52(tt, isNat(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U31(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U52(tt, isNat(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U52(tt, isNat(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U52(tt, isNat(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U52(tt, isNat(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U52(tt, isNat(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__isNat(x0)), MARK(U32(z0))) A__U52(tt, isNat(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__isNat(x0)), MARK(U41(z0, z1))) A__U52(tt, isNat(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__isNat(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, isNat(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__isNat(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, isNat(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U52(tt, isNat(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__isNat(x0)), MARK(U61(z0))) A__U52(tt, isNat(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__isNat(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, isNat(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__isNat(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, isNat(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1))) A__U52(tt, isNat(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U52(tt, isNat(0), x1) -> c14(MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(MARK(x1)) A__U52(tt, isNat(x0), tt) -> c14(A__PLUS(tt, a__isNat(x0))) A__U52(tt, isNat(x0), 0) -> c14(A__PLUS(0, a__isNat(x0))) A__U52(tt, U21(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U21(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U52(tt, U21(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U21(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U21(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U21(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U21(U71(z0, z1, z2)), x1) -> 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U32(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U32(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U32(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U32(mark(x0))), MARK(s(z0))) A__U52(tt, U32(x0), x1) -> c14(MARK(x1)) A__U52(tt, U32(x0), tt) -> c14(A__PLUS(tt, a__U32(mark(x0)))) A__U52(tt, U32(x0), 0) -> c14(A__PLUS(0, a__U32(mark(x0)))) A__U52(tt, U41(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U41(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U41(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U41(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U41(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U41(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U41(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U41(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U41(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U41(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U41(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U41(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U41(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U41(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U41(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U41(tt, x1)), MARK(x2)) A__U52(tt, U41(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U41(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U41(0, x1)), MARK(x2)) A__U52(tt, U41(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U41(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U41(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U41(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U41(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U41(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U41(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U41(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U41(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U41(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U41(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U41(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U41(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U41(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U41(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U41(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U41(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U41(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U41(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U41(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U41(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U41(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U41(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U41(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U41(x0, x1), tt) -> c14(A__PLUS(tt, a__U41(mark(x0), x1))) A__U52(tt, U41(x0, x1), 0) -> c14(A__PLUS(0, a__U41(mark(x0), x1))) A__U52(tt, U51(x0, z1, z2), x3) -> c14(A__PLUS(mark(x3), U51(mark(x0), z1, z2)), MARK(x3)) A__U52(tt, U51(U11(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U52(tt, U51(U12(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U51(isNat(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__isNat(z0), x1, x2)), MARK(x3)) A__U52(tt, U51(U21(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U51(U31(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U52(tt, U51(U32(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U32(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U51(U41(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U41(mark(z0), z1), x1, x2)), MARK(x3)) A__U52(tt, U51(U51(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U51(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U51(U52(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U52(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U51(plus(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U52(tt, U51(U61(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U61(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U51(U71(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U71(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U51(U72(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U72(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U51(x(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U52(tt, U51(tt, x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(tt, x1, x2)), MARK(x3)) A__U52(tt, U51(s(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(s(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U51(0, x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(0, x1, x2)), MARK(x3)) A__U52(tt, U51(x0, x1, x2), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U51(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U52(tt, U51(x0, x1, x2), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(U12(z0))) A__U52(tt, U51(x0, x1, x2), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U51(mark(x0), x1, x2)), MARK(isNat(z0))) A__U52(tt, U51(x0, x1, x2), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(U21(z0))) A__U52(tt, U51(x0, x1, x2), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U51(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U52(tt, U51(x0, x1, x2), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(U32(z0))) A__U52(tt, U51(x0, x1, x2), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U51(mark(x0), x1, x2)), MARK(U41(z0, z1))) A__U52(tt, U51(x0, x1, x2), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U51(mark(x0), x1, x2)), MARK(U51(z0, z1, z2))) A__U52(tt, U51(x0, x1, x2), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U51(mark(x0), x1, x2)), MARK(U52(z0, z1, z2))) A__U52(tt, U51(x0, x1, x2), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U51(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U52(tt, U51(x0, x1, x2), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(U61(z0))) A__U52(tt, U51(x0, x1, x2), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U51(mark(x0), x1, x2)), MARK(U71(z0, z1, z2))) A__U52(tt, U51(x0, x1, x2), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U51(mark(x0), x1, x2)), MARK(U72(z0, z1, z2))) A__U52(tt, U51(x0, x1, x2), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U51(mark(x0), x1, x2)), MARK(x(z0, z1))) A__U52(tt, U51(x0, x1, x2), tt) -> c14(A__PLUS(tt, a__U51(mark(x0), x1, x2)), MARK(tt)) A__U52(tt, U51(x0, x1, x2), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(s(z0))) A__U52(tt, U51(x0, x1, x2), 0) -> c14(A__PLUS(0, a__U51(mark(x0), x1, x2)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2, c43_1, c44_2, c44_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c49_2, c49_1, c50_2, c50_1, c51_2, c51_1, c12_2 ---------------------------------------- (217) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (218) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, 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c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, s(x1)) -> c12(A__ISNAT(s(x1))) A__U51(tt, x0, x(0, x2)) -> c12(A__U52(a__U31(tt, x2), x0, x(0, x2)), A__ISNAT(x(0, x2))) A__U51(tt, x0, x(plus(z0, z1), x2)) -> c12(A__U52(a__U31(a__U11(a__isNat(z0), z1), x2), x0, x(plus(z0, z1), x2)), A__ISNAT(x(plus(z0, z1), x2))) A__U51(tt, x0, x(s(z0), x2)) -> c12(A__U52(a__U31(a__U21(a__isNat(z0)), x2), x0, x(s(z0), x2)), A__ISNAT(x(s(z0), x2))) A__U51(tt, x0, x(x(z0, z1), x2)) -> c12(A__U52(a__U31(a__U31(a__isNat(z0), z1), x2), x0, x(x(z0, z1), x2)), A__ISNAT(x(x(z0, z1), x2))) A__U51(tt, x0, x(z0, x2)) -> c12(A__U52(a__U31(isNat(z0), x2), x0, x(z0, x2)), A__ISNAT(x(z0, x2))) A__U51(tt, x0, x(x1, z1)) -> c12(A__ISNAT(x(x1, z1))) A__U52(tt, U11(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U11(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U52(tt, U11(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U52(tt, U11(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U11(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U11(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U11(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U11(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U11(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U11(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U11(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U11(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U11(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U11(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U11(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U11(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U11(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U11(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U11(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U11(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U11(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U11(x0, x1), tt) -> c14(A__PLUS(tt, a__U11(mark(x0), x1))) A__U52(tt, U11(x0, x1), 0) -> c14(A__PLUS(0, a__U11(mark(x0), x1))) A__U52(tt, U12(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U12(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U52(tt, U12(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U12(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U12(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U12(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(tt), x1) -> c14(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U52(tt, U12(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U52(tt, U12(0), x1) -> c14(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U52(tt, U12(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U12(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U52(tt, U12(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U52(tt, U12(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U52(tt, U12(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U12(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U12(mark(x0))), MARK(U32(z0))) A__U52(tt, U12(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U12(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U12(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U12(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U12(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U12(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U12(mark(x0))), MARK(U61(z0))) A__U52(tt, U12(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U12(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U12(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U12(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U12(mark(x0))), 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A__U52(tt, U41(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U41(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U41(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U41(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U41(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U41(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U41(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U41(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U41(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U41(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U41(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U41(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U41(tt, x1)), MARK(x2)) A__U52(tt, U41(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U41(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U41(0, x1)), MARK(x2)) A__U52(tt, U41(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U41(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U41(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U41(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U41(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U41(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U41(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U41(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U41(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U41(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U41(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U41(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U41(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U41(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U41(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U41(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U41(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U41(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U41(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U41(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U41(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U41(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U41(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U41(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U41(x0, x1), tt) -> c14(A__PLUS(tt, a__U41(mark(x0), x1))) A__U52(tt, U41(x0, x1), 0) -> c14(A__PLUS(0, a__U41(mark(x0), x1))) A__U52(tt, U51(U11(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U52(tt, U51(U12(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U51(isNat(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__isNat(z0), x1, x2)), MARK(x3)) A__U52(tt, U51(U21(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U51(U31(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U52(tt, U51(U32(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U32(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U51(U41(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U41(mark(z0), z1), x1, x2)), MARK(x3)) A__U52(tt, U51(U51(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U51(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U51(U52(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U52(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U51(plus(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U52(tt, U51(U61(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U61(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U51(U71(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U71(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U51(U72(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U72(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U51(x(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U52(tt, U51(tt, x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(tt, x1, x2)), MARK(x3)) A__U52(tt, U51(s(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(s(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U51(0, x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(0, x1, x2)), MARK(x3)) A__U52(tt, U51(x0, x1, x2), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U51(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U52(tt, U51(x0, x1, x2), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(U12(z0))) A__U52(tt, U51(x0, x1, x2), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U51(mark(x0), x1, x2)), MARK(isNat(z0))) A__U52(tt, U51(x0, x1, x2), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(U21(z0))) A__U52(tt, U51(x0, x1, x2), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U51(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U52(tt, U51(x0, x1, x2), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(U32(z0))) A__U52(tt, U51(x0, x1, x2), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U51(mark(x0), x1, x2)), MARK(U41(z0, z1))) A__U52(tt, U51(x0, x1, x2), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U51(mark(x0), x1, x2)), MARK(U51(z0, z1, z2))) A__U52(tt, U51(x0, x1, x2), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U51(mark(x0), x1, x2)), MARK(U52(z0, z1, z2))) A__U52(tt, U51(x0, x1, x2), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U51(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U52(tt, U51(x0, x1, x2), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(U61(z0))) A__U52(tt, U51(x0, x1, x2), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U51(mark(x0), x1, x2)), MARK(U71(z0, z1, z2))) A__U52(tt, U51(x0, x1, x2), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U51(mark(x0), x1, x2)), MARK(U72(z0, z1, z2))) A__U52(tt, U51(x0, x1, x2), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U51(mark(x0), x1, x2)), MARK(x(z0, z1))) A__U52(tt, U51(x0, x1, x2), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(s(z0))) A__U52(tt, U51(x0, z1, z2), x3) -> c14(MARK(x3)) A__U52(tt, U51(x0, x1, x2), tt) -> c14(A__PLUS(tt, a__U51(mark(x0), x1, x2))) A__U52(tt, U51(x0, x1, x2), 0) -> c14(A__PLUS(0, a__U51(mark(x0), x1, x2))) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, s(x1)) -> c12(A__ISNAT(s(x1))) A__U51(tt, x0, x(0, x2)) -> c12(A__U52(a__U31(tt, x2), x0, x(0, x2)), A__ISNAT(x(0, x2))) A__U51(tt, x0, x(plus(z0, z1), x2)) -> c12(A__U52(a__U31(a__U11(a__isNat(z0), z1), x2), x0, x(plus(z0, z1), x2)), A__ISNAT(x(plus(z0, z1), x2))) A__U51(tt, x0, x(s(z0), x2)) -> c12(A__U52(a__U31(a__U21(a__isNat(z0)), x2), x0, x(s(z0), x2)), A__ISNAT(x(s(z0), x2))) A__U51(tt, x0, x(x(z0, z1), x2)) -> c12(A__U52(a__U31(a__U31(a__isNat(z0), z1), x2), x0, x(x(z0, z1), x2)), A__ISNAT(x(x(z0, z1), x2))) A__U51(tt, x0, x(z0, x2)) -> c12(A__U52(a__U31(isNat(z0), x2), x0, x(z0, x2)), A__ISNAT(x(z0, x2))) A__U51(tt, x0, x(x1, z1)) -> c12(A__ISNAT(x(x1, z1))) A__U52(tt, U11(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U11(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U52(tt, U11(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U52(tt, U11(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U11(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U11(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U11(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U11(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U11(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U11(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U11(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U11(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U11(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U11(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U11(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U11(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U11(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U11(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U11(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U11(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U11(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U11(x0, x1), tt) -> c14(A__PLUS(tt, a__U11(mark(x0), x1))) A__U52(tt, U11(x0, x1), 0) -> c14(A__PLUS(0, a__U11(mark(x0), x1))) A__U52(tt, U12(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U12(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U52(tt, U12(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U12(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U12(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U12(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(tt), x1) -> c14(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U52(tt, U12(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U52(tt, U12(0), x1) -> c14(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U52(tt, U12(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U12(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U52(tt, U12(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U52(tt, U12(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U52(tt, U12(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U12(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U12(mark(x0))), MARK(U32(z0))) A__U52(tt, U12(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U12(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U12(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U12(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U12(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U12(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U12(mark(x0))), MARK(U61(z0))) A__U52(tt, U12(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U12(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U12(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U12(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U52(tt, U12(x0), x1) -> c14(MARK(x1)) A__U52(tt, U12(x0), tt) -> c14(A__PLUS(tt, a__U12(mark(x0)))) A__U52(tt, U12(x0), 0) -> c14(A__PLUS(0, a__U12(mark(x0)))) A__U52(tt, isNat(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U52(tt, isNat(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U31(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U52(tt, isNat(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U52(tt, isNat(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U52(tt, isNat(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U52(tt, isNat(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U52(tt, isNat(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__isNat(x0)), MARK(U32(z0))) A__U52(tt, isNat(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__isNat(x0)), MARK(U41(z0, z1))) A__U52(tt, isNat(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__isNat(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, isNat(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__isNat(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, isNat(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U52(tt, isNat(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__isNat(x0)), MARK(U61(z0))) A__U52(tt, isNat(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__isNat(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, isNat(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__isNat(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, isNat(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1))) A__U52(tt, isNat(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U52(tt, isNat(0), x1) -> c14(MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(MARK(x1)) A__U52(tt, isNat(x0), tt) -> c14(A__PLUS(tt, a__isNat(x0))) A__U52(tt, isNat(x0), 0) -> c14(A__PLUS(0, a__isNat(x0))) A__U52(tt, U21(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U21(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U52(tt, U21(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U21(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U21(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U21(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U21(U71(z0, z1, z2)), x1) -> 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U32(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U32(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U32(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U32(mark(x0))), MARK(s(z0))) A__U52(tt, U32(x0), x1) -> c14(MARK(x1)) A__U52(tt, U32(x0), tt) -> c14(A__PLUS(tt, a__U32(mark(x0)))) A__U52(tt, U32(x0), 0) -> c14(A__PLUS(0, a__U32(mark(x0)))) A__U52(tt, U41(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U41(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U41(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U41(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U41(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U41(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U41(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U41(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U41(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U41(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U41(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U41(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U41(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U41(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U41(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U41(tt, x1)), MARK(x2)) A__U52(tt, U41(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U41(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U41(0, x1)), MARK(x2)) A__U52(tt, U41(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U41(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U41(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U41(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U41(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U41(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U41(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U41(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U41(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U41(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U41(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U41(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U41(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U41(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U41(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U41(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U41(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U41(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U41(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U41(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U41(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U41(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U41(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U41(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U41(x0, x1), tt) -> c14(A__PLUS(tt, a__U41(mark(x0), x1))) A__U52(tt, U41(x0, x1), 0) -> c14(A__PLUS(0, a__U41(mark(x0), x1))) A__U52(tt, U51(U11(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U52(tt, U51(U12(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U51(isNat(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__isNat(z0), x1, x2)), MARK(x3)) A__U52(tt, U51(U21(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U51(U31(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U52(tt, U51(U32(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U32(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U51(U41(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U41(mark(z0), z1), x1, x2)), MARK(x3)) A__U52(tt, U51(U51(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U51(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U51(U52(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U52(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U51(plus(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U52(tt, U51(U61(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U61(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U51(U71(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U71(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U51(U72(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U72(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U51(x(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U52(tt, U51(tt, x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(tt, x1, x2)), MARK(x3)) A__U52(tt, U51(s(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(s(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U51(0, x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(0, x1, x2)), MARK(x3)) A__U52(tt, U51(x0, x1, x2), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U51(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U52(tt, U51(x0, x1, x2), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(U12(z0))) A__U52(tt, U51(x0, x1, x2), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U51(mark(x0), x1, x2)), MARK(isNat(z0))) A__U52(tt, U51(x0, x1, x2), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(U21(z0))) A__U52(tt, U51(x0, x1, x2), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U51(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U52(tt, U51(x0, x1, x2), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(U32(z0))) A__U52(tt, U51(x0, x1, x2), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U51(mark(x0), x1, x2)), MARK(U41(z0, z1))) A__U52(tt, U51(x0, x1, x2), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U51(mark(x0), x1, x2)), MARK(U51(z0, z1, z2))) A__U52(tt, U51(x0, x1, x2), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U51(mark(x0), x1, x2)), MARK(U52(z0, z1, z2))) A__U52(tt, U51(x0, x1, x2), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U51(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U52(tt, U51(x0, x1, x2), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(U61(z0))) A__U52(tt, U51(x0, x1, x2), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U51(mark(x0), x1, x2)), MARK(U71(z0, z1, z2))) A__U52(tt, U51(x0, x1, x2), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U51(mark(x0), x1, x2)), MARK(U72(z0, z1, z2))) A__U52(tt, U51(x0, x1, x2), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U51(mark(x0), x1, x2)), MARK(x(z0, z1))) A__U52(tt, U51(x0, x1, x2), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(s(z0))) A__U52(tt, U51(x0, z1, z2), x3) -> c14(MARK(x3)) A__U52(tt, U51(x0, x1, x2), tt) -> c14(A__PLUS(tt, a__U51(mark(x0), x1, x2))) A__U52(tt, U51(x0, x1, x2), 0) -> c14(A__PLUS(0, a__U51(mark(x0), x1, x2))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2, c43_1, c44_2, c44_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c49_2, c49_1, c50_2, c50_1, c51_2, c51_1, c12_2 ---------------------------------------- (219) CdtNarrowingProof (BOTH BOUNDS(ID, ID)) Use narrowing to replace A__U52(tt, U52(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(x1)) by A__U52(tt, U52(x0, z1, z2), x3) -> c14(A__PLUS(mark(x3), U52(mark(x0), z1, z2)), MARK(x3)) A__U52(tt, U52(U11(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U52(tt, U52(U12(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U52(isNat(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__isNat(z0), x1, x2)), MARK(x3)) A__U52(tt, U52(U21(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U52(U31(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U52(tt, U52(U32(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U32(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U52(U41(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U41(mark(z0), z1), x1, x2)), MARK(x3)) A__U52(tt, U52(U51(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U51(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U52(U52(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U52(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U52(plus(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U52(tt, U52(U61(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U61(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U52(U71(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U71(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U52(U72(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U72(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U52(x(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U52(tt, U52(tt, x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(tt, x1, x2)), MARK(x3)) A__U52(tt, U52(s(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(s(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U52(0, x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(0, x1, x2)), MARK(x3)) A__U52(tt, U52(x0, x1, x2), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U52(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U52(tt, U52(x0, x1, x2), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U52(mark(x0), x1, x2)), MARK(U12(z0))) A__U52(tt, U52(x0, x1, x2), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U52(mark(x0), x1, x2)), MARK(isNat(z0))) A__U52(tt, U52(x0, x1, x2), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U52(mark(x0), x1, x2)), MARK(U21(z0))) A__U52(tt, U52(x0, x1, x2), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U52(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U52(tt, U52(x0, x1, x2), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U52(mark(x0), x1, x2)), MARK(U32(z0))) A__U52(tt, U52(x0, x1, x2), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U52(mark(x0), x1, x2)), MARK(U41(z0, z1))) A__U52(tt, U52(x0, x1, x2), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U52(mark(x0), x1, x2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(x0, x1, x2), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U52(mark(x0), x1, x2)), MARK(U52(z0, z1, z2))) A__U52(tt, U52(x0, x1, x2), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U52(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U52(tt, U52(x0, x1, x2), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U52(mark(x0), x1, x2)), MARK(U61(z0))) A__U52(tt, U52(x0, x1, x2), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U52(mark(x0), x1, x2)), MARK(U71(z0, z1, z2))) A__U52(tt, U52(x0, x1, x2), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U52(mark(x0), x1, x2)), MARK(U72(z0, z1, z2))) A__U52(tt, U52(x0, x1, x2), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U52(mark(x0), x1, x2)), MARK(x(z0, z1))) A__U52(tt, U52(x0, x1, x2), tt) -> c14(A__PLUS(tt, a__U52(mark(x0), x1, x2)), MARK(tt)) A__U52(tt, U52(x0, x1, x2), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U52(mark(x0), x1, x2)), MARK(s(z0))) A__U52(tt, U52(x0, x1, x2), 0) -> c14(A__PLUS(0, a__U52(mark(x0), x1, x2)), MARK(0)) ---------------------------------------- (220) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, s(x1)) -> c12(A__ISNAT(s(x1))) A__U51(tt, x0, x(0, x2)) -> c12(A__U52(a__U31(tt, x2), x0, x(0, x2)), A__ISNAT(x(0, x2))) A__U51(tt, x0, x(plus(z0, z1), x2)) -> c12(A__U52(a__U31(a__U11(a__isNat(z0), z1), x2), x0, x(plus(z0, z1), x2)), A__ISNAT(x(plus(z0, z1), x2))) A__U51(tt, x0, x(s(z0), x2)) -> c12(A__U52(a__U31(a__U21(a__isNat(z0)), x2), x0, x(s(z0), x2)), A__ISNAT(x(s(z0), x2))) A__U51(tt, x0, x(x(z0, z1), x2)) -> c12(A__U52(a__U31(a__U31(a__isNat(z0), z1), x2), x0, x(x(z0, z1), x2)), A__ISNAT(x(x(z0, z1), x2))) A__U51(tt, x0, x(z0, x2)) -> c12(A__U52(a__U31(isNat(z0), x2), x0, x(z0, x2)), A__ISNAT(x(z0, x2))) A__U51(tt, x0, x(x1, z1)) -> c12(A__ISNAT(x(x1, z1))) A__U52(tt, U11(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U11(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U52(tt, U11(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U52(tt, U11(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U11(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U11(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U11(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U11(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U11(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U11(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U11(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U11(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U11(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U11(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U11(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U11(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U11(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U11(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U11(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U11(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U11(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U11(x0, x1), tt) -> c14(A__PLUS(tt, a__U11(mark(x0), x1))) A__U52(tt, U11(x0, x1), 0) -> c14(A__PLUS(0, a__U11(mark(x0), x1))) A__U52(tt, U12(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, 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U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U52(tt, U21(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U52(tt, U21(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U52(tt, U21(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U21(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U21(mark(x0))), MARK(U32(z0))) A__U52(tt, U21(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U21(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U21(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U21(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U21(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U21(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U21(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U21(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), 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x2)), MARK(x3)) A__U52(tt, U51(U41(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U41(mark(z0), z1), x1, x2)), MARK(x3)) A__U52(tt, U51(U51(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U51(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U51(U52(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U52(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U51(plus(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U52(tt, U51(U61(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U61(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U51(U71(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U71(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U51(U72(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U72(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U51(x(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U52(tt, U51(tt, x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(tt, x1, x2)), MARK(x3)) A__U52(tt, U51(s(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(s(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U51(0, x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(0, x1, x2)), MARK(x3)) A__U52(tt, U51(x0, x1, x2), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U51(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U52(tt, U51(x0, x1, x2), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(U12(z0))) A__U52(tt, U51(x0, x1, x2), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U51(mark(x0), x1, x2)), MARK(isNat(z0))) A__U52(tt, U51(x0, x1, x2), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(U21(z0))) A__U52(tt, U51(x0, x1, x2), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U51(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U52(tt, U51(x0, x1, x2), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(U32(z0))) A__U52(tt, U51(x0, x1, x2), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U51(mark(x0), x1, x2)), MARK(U41(z0, z1))) A__U52(tt, U51(x0, x1, x2), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U51(mark(x0), x1, x2)), MARK(U51(z0, z1, z2))) A__U52(tt, U51(x0, x1, x2), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U51(mark(x0), x1, x2)), MARK(U52(z0, z1, z2))) A__U52(tt, U51(x0, x1, x2), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U51(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U52(tt, U51(x0, x1, x2), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(U61(z0))) A__U52(tt, U51(x0, x1, x2), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U51(mark(x0), x1, x2)), MARK(U71(z0, z1, z2))) A__U52(tt, U51(x0, x1, x2), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U51(mark(x0), x1, x2)), MARK(U72(z0, z1, z2))) A__U52(tt, U51(x0, x1, x2), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U51(mark(x0), x1, x2)), MARK(x(z0, z1))) A__U52(tt, U51(x0, x1, x2), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(s(z0))) A__U52(tt, U51(x0, z1, z2), x3) -> c14(MARK(x3)) A__U52(tt, U51(x0, x1, x2), tt) -> c14(A__PLUS(tt, a__U51(mark(x0), x1, x2))) A__U52(tt, U51(x0, x1, x2), 0) -> c14(A__PLUS(0, a__U51(mark(x0), x1, x2))) A__U52(tt, U52(x0, z1, z2), x3) -> c14(A__PLUS(mark(x3), U52(mark(x0), z1, z2)), MARK(x3)) A__U52(tt, U52(U11(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U52(tt, U52(U12(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U52(isNat(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__isNat(z0), x1, x2)), MARK(x3)) A__U52(tt, U52(U21(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U52(U31(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U52(tt, U52(U32(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U32(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U52(U41(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U41(mark(z0), z1), x1, x2)), MARK(x3)) A__U52(tt, U52(U51(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U51(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U52(U52(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U52(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U52(plus(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U52(tt, U52(U61(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U61(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U52(U71(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U71(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U52(U72(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U72(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U52(x(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U52(tt, U52(tt, x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(tt, x1, x2)), MARK(x3)) A__U52(tt, U52(s(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(s(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U52(0, x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(0, x1, x2)), MARK(x3)) A__U52(tt, U52(x0, x1, x2), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U52(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U52(tt, U52(x0, x1, x2), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U52(mark(x0), x1, x2)), MARK(U12(z0))) A__U52(tt, U52(x0, x1, x2), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U52(mark(x0), x1, x2)), MARK(isNat(z0))) A__U52(tt, U52(x0, x1, x2), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U52(mark(x0), x1, x2)), MARK(U21(z0))) A__U52(tt, U52(x0, x1, x2), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U52(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U52(tt, U52(x0, x1, x2), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U52(mark(x0), x1, x2)), MARK(U32(z0))) A__U52(tt, U52(x0, x1, x2), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U52(mark(x0), x1, x2)), MARK(U41(z0, z1))) A__U52(tt, U52(x0, x1, x2), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U52(mark(x0), x1, x2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(x0, x1, x2), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U52(mark(x0), x1, x2)), MARK(U52(z0, z1, z2))) A__U52(tt, U52(x0, x1, x2), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U52(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U52(tt, U52(x0, x1, x2), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U52(mark(x0), x1, x2)), MARK(U61(z0))) A__U52(tt, U52(x0, x1, x2), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U52(mark(x0), x1, x2)), MARK(U71(z0, z1, z2))) A__U52(tt, U52(x0, x1, x2), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U52(mark(x0), x1, x2)), MARK(U72(z0, z1, z2))) A__U52(tt, U52(x0, x1, x2), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U52(mark(x0), x1, x2)), MARK(x(z0, z1))) A__U52(tt, U52(x0, x1, x2), tt) -> c14(A__PLUS(tt, a__U52(mark(x0), x1, x2)), MARK(tt)) A__U52(tt, U52(x0, x1, x2), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U52(mark(x0), x1, x2)), MARK(s(z0))) A__U52(tt, U52(x0, x1, x2), 0) -> c14(A__PLUS(0, a__U52(mark(x0), x1, x2)), MARK(0)) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, s(x1)) -> c12(A__ISNAT(s(x1))) A__U51(tt, x0, x(0, x2)) -> c12(A__U52(a__U31(tt, x2), x0, x(0, x2)), A__ISNAT(x(0, x2))) A__U51(tt, x0, x(plus(z0, z1), x2)) -> c12(A__U52(a__U31(a__U11(a__isNat(z0), z1), x2), x0, x(plus(z0, z1), x2)), A__ISNAT(x(plus(z0, z1), x2))) A__U51(tt, x0, x(s(z0), x2)) -> c12(A__U52(a__U31(a__U21(a__isNat(z0)), x2), x0, x(s(z0), x2)), A__ISNAT(x(s(z0), x2))) A__U51(tt, x0, x(x(z0, z1), x2)) -> c12(A__U52(a__U31(a__U31(a__isNat(z0), z1), x2), x0, x(x(z0, z1), x2)), A__ISNAT(x(x(z0, z1), x2))) A__U51(tt, x0, x(z0, x2)) -> c12(A__U52(a__U31(isNat(z0), x2), x0, x(z0, x2)), A__ISNAT(x(z0, x2))) A__U51(tt, x0, x(x1, z1)) -> c12(A__ISNAT(x(x1, z1))) A__U52(tt, U11(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U11(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U52(tt, U11(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U52(tt, U11(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U11(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U11(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U11(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U11(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U11(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U11(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U11(x0, x1), U41(z0, 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c14(MARK(x1)) A__U52(tt, U32(x0), tt) -> c14(A__PLUS(tt, a__U32(mark(x0)))) A__U52(tt, U32(x0), 0) -> c14(A__PLUS(0, a__U32(mark(x0)))) A__U52(tt, U41(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U41(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U41(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U41(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U41(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U41(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U41(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U41(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U41(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U41(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U41(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U41(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U41(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U41(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U41(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U41(tt, x1)), MARK(x2)) A__U52(tt, U41(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U41(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U41(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U41(0, x1)), MARK(x2)) A__U52(tt, U41(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U41(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U41(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U41(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U41(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U41(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U41(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U41(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U41(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U41(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U41(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U41(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U41(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U41(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U41(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U41(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U41(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U41(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U41(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U41(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U41(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U41(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U41(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U41(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U41(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U41(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U41(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U41(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U41(x0, x1), tt) -> c14(A__PLUS(tt, a__U41(mark(x0), x1))) A__U52(tt, U41(x0, x1), 0) -> c14(A__PLUS(0, a__U41(mark(x0), x1))) A__U52(tt, U51(U11(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U52(tt, U51(U12(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U51(isNat(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__isNat(z0), x1, x2)), MARK(x3)) A__U52(tt, U51(U21(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U51(U31(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U52(tt, U51(U32(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U32(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U51(U41(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U41(mark(z0), z1), x1, x2)), MARK(x3)) A__U52(tt, U51(U51(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U51(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U51(U52(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U52(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U51(plus(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U52(tt, U51(U61(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U61(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U51(U71(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U71(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U51(U72(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U72(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U51(x(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U52(tt, U51(tt, x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(tt, x1, x2)), MARK(x3)) A__U52(tt, U51(s(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(s(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U51(0, x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(0, x1, x2)), MARK(x3)) A__U52(tt, U51(x0, x1, x2), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U51(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U52(tt, U51(x0, x1, x2), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(U12(z0))) A__U52(tt, U51(x0, x1, x2), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U51(mark(x0), x1, x2)), MARK(isNat(z0))) A__U52(tt, U51(x0, x1, x2), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(U21(z0))) A__U52(tt, U51(x0, x1, x2), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U51(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U52(tt, U51(x0, x1, x2), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(U32(z0))) A__U52(tt, U51(x0, x1, x2), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U51(mark(x0), x1, x2)), MARK(U41(z0, z1))) A__U52(tt, U51(x0, x1, x2), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U51(mark(x0), x1, x2)), MARK(U51(z0, z1, z2))) A__U52(tt, U51(x0, x1, x2), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U51(mark(x0), x1, x2)), MARK(U52(z0, z1, z2))) A__U52(tt, U51(x0, x1, x2), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U51(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U52(tt, U51(x0, x1, x2), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(U61(z0))) A__U52(tt, U51(x0, x1, x2), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U51(mark(x0), x1, x2)), MARK(U71(z0, z1, z2))) A__U52(tt, U51(x0, x1, x2), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U51(mark(x0), x1, x2)), MARK(U72(z0, z1, z2))) A__U52(tt, U51(x0, x1, x2), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U51(mark(x0), x1, x2)), MARK(x(z0, z1))) A__U52(tt, U51(x0, x1, x2), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(s(z0))) A__U52(tt, U51(x0, z1, z2), x3) -> c14(MARK(x3)) A__U52(tt, U51(x0, x1, x2), tt) -> c14(A__PLUS(tt, a__U51(mark(x0), x1, x2))) A__U52(tt, U51(x0, x1, x2), 0) -> c14(A__PLUS(0, a__U51(mark(x0), x1, x2))) A__U52(tt, U52(x0, z1, z2), x3) -> c14(A__PLUS(mark(x3), U52(mark(x0), z1, z2)), MARK(x3)) A__U52(tt, U52(U11(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U52(tt, U52(U12(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U52(isNat(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__isNat(z0), x1, x2)), MARK(x3)) A__U52(tt, U52(U21(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U52(U31(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U52(tt, U52(U32(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U32(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U52(U41(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U41(mark(z0), z1), x1, x2)), MARK(x3)) A__U52(tt, U52(U51(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U51(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U52(U52(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U52(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U52(plus(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U52(tt, U52(U61(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U61(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U52(U71(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U71(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U52(U72(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U72(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U52(x(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U52(tt, U52(tt, x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(tt, x1, x2)), MARK(x3)) A__U52(tt, U52(s(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(s(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U52(0, x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(0, x1, x2)), MARK(x3)) A__U52(tt, U52(x0, x1, x2), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U52(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U52(tt, U52(x0, x1, x2), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U52(mark(x0), x1, x2)), MARK(U12(z0))) A__U52(tt, U52(x0, x1, x2), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U52(mark(x0), x1, x2)), MARK(isNat(z0))) A__U52(tt, U52(x0, x1, x2), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U52(mark(x0), x1, x2)), MARK(U21(z0))) A__U52(tt, U52(x0, x1, x2), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U52(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U52(tt, U52(x0, x1, x2), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U52(mark(x0), x1, x2)), MARK(U32(z0))) A__U52(tt, U52(x0, x1, x2), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U52(mark(x0), x1, x2)), MARK(U41(z0, z1))) A__U52(tt, U52(x0, x1, x2), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U52(mark(x0), x1, x2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(x0, x1, x2), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U52(mark(x0), x1, x2)), MARK(U52(z0, z1, z2))) A__U52(tt, U52(x0, x1, x2), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U52(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U52(tt, U52(x0, x1, x2), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U52(mark(x0), x1, x2)), MARK(U61(z0))) A__U52(tt, U52(x0, x1, x2), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U52(mark(x0), x1, x2)), MARK(U71(z0, z1, z2))) A__U52(tt, U52(x0, x1, x2), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U52(mark(x0), x1, x2)), MARK(U72(z0, z1, z2))) A__U52(tt, U52(x0, x1, x2), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U52(mark(x0), x1, x2)), MARK(x(z0, z1))) A__U52(tt, U52(x0, x1, x2), tt) -> c14(A__PLUS(tt, a__U52(mark(x0), x1, x2)), MARK(tt)) A__U52(tt, U52(x0, x1, x2), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U52(mark(x0), x1, x2)), MARK(s(z0))) A__U52(tt, U52(x0, x1, x2), 0) -> c14(A__PLUS(0, a__U52(mark(x0), x1, x2)), MARK(0)) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2, c43_1, c44_2, c44_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c49_2, c49_1, c50_2, c50_1, c51_2, c51_1, c12_2 ---------------------------------------- (221) CdtRhsSimplificationProcessorProof (BOTH BOUNDS(ID, ID)) Removed 3 trailing tuple parts ---------------------------------------- (222) Obligation: Complexity Dependency Tuples Problem Rules: a__U11(tt, z0) -> a__U12(a__isNat(z0)) a__U11(z0, z1) -> U11(z0, z1) a__U12(tt) -> tt a__U12(z0) -> U12(z0) a__U21(tt) -> tt a__U21(z0) -> U21(z0) a__U31(tt, z0) -> a__U32(a__isNat(z0)) a__U31(z0, z1) -> U31(z0, z1) a__U32(tt) -> tt a__U32(z0) -> U32(z0) a__U41(tt, z0) -> mark(z0) a__U41(z0, z1) -> U41(z0, z1) a__U51(tt, z0, z1) -> a__U52(a__isNat(z1), z0, z1) a__U51(z0, z1, z2) -> U51(z0, z1, z2) a__U52(tt, z0, z1) -> s(a__plus(mark(z1), mark(z0))) a__U52(z0, z1, z2) -> U52(z0, z1, z2) a__U61(tt) -> 0 a__U61(z0) -> U61(z0) a__U71(tt, z0, z1) -> a__U72(a__isNat(z1), z0, z1) a__U71(z0, z1, z2) -> U71(z0, z1, z2) a__U72(tt, z0, z1) -> a__plus(a__x(mark(z1), mark(z0)), mark(z1)) a__U72(z0, z1, z2) -> U72(z0, z1, z2) a__isNat(0) -> tt a__isNat(plus(z0, z1)) -> a__U11(a__isNat(z0), z1) a__isNat(s(z0)) -> a__U21(a__isNat(z0)) a__isNat(x(z0, z1)) -> a__U31(a__isNat(z0), z1) a__isNat(z0) -> isNat(z0) a__plus(z0, 0) -> a__U41(a__isNat(z0), z0) a__plus(z0, s(z1)) -> a__U51(a__isNat(z1), z1, z0) a__plus(z0, z1) -> plus(z0, z1) a__x(z0, 0) -> a__U61(a__isNat(z0)) a__x(z0, s(z1)) -> a__U71(a__isNat(z1), z1, z0) a__x(z0, z1) -> x(z0, z1) mark(U11(z0, z1)) -> a__U11(mark(z0), z1) mark(U12(z0)) -> a__U12(mark(z0)) mark(isNat(z0)) -> a__isNat(z0) mark(U21(z0)) -> a__U21(mark(z0)) mark(U31(z0, z1)) -> a__U31(mark(z0), z1) mark(U32(z0)) -> a__U32(mark(z0)) mark(U41(z0, z1)) -> a__U41(mark(z0), z1) mark(U51(z0, z1, z2)) -> a__U51(mark(z0), z1, z2) mark(U52(z0, z1, z2)) -> a__U52(mark(z0), z1, z2) mark(plus(z0, z1)) -> a__plus(mark(z0), mark(z1)) mark(U61(z0)) -> a__U61(mark(z0)) mark(U71(z0, z1, z2)) -> a__U71(mark(z0), z1, z2) mark(U72(z0, z1, z2)) -> a__U72(mark(z0), z1, z2) mark(x(z0, z1)) -> a__x(mark(z0), mark(z1)) mark(tt) -> tt mark(s(z0)) -> s(mark(z0)) mark(0) -> 0 Tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, s(x1)) -> c12(A__ISNAT(s(x1))) A__U51(tt, x0, x(0, x2)) -> c12(A__U52(a__U31(tt, x2), x0, x(0, x2)), A__ISNAT(x(0, x2))) A__U51(tt, x0, x(plus(z0, z1), x2)) -> c12(A__U52(a__U31(a__U11(a__isNat(z0), z1), x2), x0, x(plus(z0, z1), x2)), A__ISNAT(x(plus(z0, z1), x2))) A__U51(tt, x0, x(s(z0), x2)) -> c12(A__U52(a__U31(a__U21(a__isNat(z0)), x2), x0, x(s(z0), x2)), A__ISNAT(x(s(z0), x2))) A__U51(tt, x0, x(x(z0, z1), x2)) -> c12(A__U52(a__U31(a__U31(a__isNat(z0), z1), x2), x0, x(x(z0, z1), x2)), A__ISNAT(x(x(z0, z1), x2))) A__U51(tt, x0, x(z0, x2)) -> c12(A__U52(a__U31(isNat(z0), x2), x0, x(z0, x2)), A__ISNAT(x(z0, x2))) A__U51(tt, x0, x(x1, z1)) -> c12(A__ISNAT(x(x1, z1))) A__U52(tt, U11(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U11(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U52(tt, U11(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U52(tt, U11(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U11(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U11(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U11(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U11(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U11(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U11(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U11(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U11(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U11(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U11(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U11(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U11(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U11(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U11(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U11(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U11(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U11(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U11(x0, x1), tt) -> c14(A__PLUS(tt, a__U11(mark(x0), x1))) A__U52(tt, U11(x0, x1), 0) -> c14(A__PLUS(0, a__U11(mark(x0), x1))) A__U52(tt, U12(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U12(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U52(tt, U12(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U12(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U12(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U12(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(tt), x1) -> c14(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U52(tt, U12(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U52(tt, U12(0), x1) -> c14(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U52(tt, U12(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U12(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U52(tt, U12(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U52(tt, U12(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U52(tt, U12(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U12(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U12(mark(x0))), MARK(U32(z0))) A__U52(tt, U12(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U12(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U12(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U12(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U12(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U12(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U12(mark(x0))), MARK(U61(z0))) A__U52(tt, U12(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U12(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U12(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U12(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U52(tt, U12(x0), x1) -> c14(MARK(x1)) A__U52(tt, U12(x0), tt) -> c14(A__PLUS(tt, a__U12(mark(x0)))) A__U52(tt, U12(x0), 0) -> c14(A__PLUS(0, a__U12(mark(x0)))) A__U52(tt, isNat(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U52(tt, isNat(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U31(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U52(tt, isNat(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U52(tt, isNat(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U52(tt, isNat(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U52(tt, isNat(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U52(tt, isNat(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__isNat(x0)), MARK(U32(z0))) A__U52(tt, isNat(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__isNat(x0)), MARK(U41(z0, z1))) A__U52(tt, isNat(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__isNat(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, isNat(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__isNat(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, isNat(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U52(tt, isNat(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__isNat(x0)), MARK(U61(z0))) A__U52(tt, isNat(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__isNat(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, isNat(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__isNat(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, isNat(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1))) A__U52(tt, isNat(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U52(tt, isNat(0), x1) -> c14(MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(MARK(x1)) A__U52(tt, isNat(x0), tt) -> c14(A__PLUS(tt, a__isNat(x0))) A__U52(tt, isNat(x0), 0) -> c14(A__PLUS(0, a__isNat(x0))) A__U52(tt, U21(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U21(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U52(tt, U21(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U21(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U21(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U21(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U21(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U21(tt), x1) -> c14(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U52(tt, U21(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U52(tt, U21(0), x1) -> c14(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U52(tt, U21(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U21(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U21(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U21(mark(x0))), MARK(U12(z0))) A__U52(tt, U21(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U21(mark(x0))), MARK(isNat(z0))) A__U52(tt, U21(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U21(mark(x0))), MARK(U21(z0))) A__U52(tt, U21(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U21(mark(x0))), MARK(U31(z0, 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MARK(x(z0, z1))) A__U52(tt, U21(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U21(mark(x0))), MARK(s(z0))) A__U52(tt, U21(x0), x1) -> c14(MARK(x1)) A__U52(tt, U21(x0), tt) -> c14(A__PLUS(tt, a__U21(mark(x0)))) A__U52(tt, U21(x0), 0) -> c14(A__PLUS(0, a__U21(mark(x0)))) A__U52(tt, U31(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U31(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U31(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U31(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U31(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U31(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, 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a__U51(a__U52(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U51(plus(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U52(tt, U51(U61(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U61(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U51(U71(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U71(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U51(U72(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U72(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U51(x(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U52(tt, U51(tt, x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(tt, x1, x2)), MARK(x3)) A__U52(tt, U51(s(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(s(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U51(0, x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(0, x1, x2)), MARK(x3)) A__U52(tt, U51(x0, x1, x2), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U51(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U52(tt, U51(x0, x1, x2), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(U12(z0))) A__U52(tt, U51(x0, x1, x2), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U51(mark(x0), x1, x2)), MARK(isNat(z0))) A__U52(tt, U51(x0, x1, x2), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(U21(z0))) A__U52(tt, U51(x0, x1, x2), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U51(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U52(tt, U51(x0, x1, x2), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(U32(z0))) A__U52(tt, U51(x0, x1, x2), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U51(mark(x0), x1, x2)), MARK(U41(z0, z1))) A__U52(tt, U51(x0, x1, x2), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U51(mark(x0), x1, x2)), MARK(U51(z0, z1, z2))) A__U52(tt, U51(x0, x1, x2), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U51(mark(x0), x1, x2)), MARK(U52(z0, z1, z2))) A__U52(tt, U51(x0, x1, x2), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U51(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U52(tt, U51(x0, x1, x2), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(U61(z0))) A__U52(tt, U51(x0, x1, x2), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U51(mark(x0), x1, x2)), MARK(U71(z0, z1, z2))) A__U52(tt, U51(x0, x1, x2), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U51(mark(x0), x1, x2)), MARK(U72(z0, z1, z2))) A__U52(tt, U51(x0, x1, x2), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U51(mark(x0), x1, x2)), MARK(x(z0, z1))) A__U52(tt, U51(x0, x1, x2), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(s(z0))) A__U52(tt, U51(x0, z1, z2), x3) -> c14(MARK(x3)) A__U52(tt, U51(x0, x1, x2), tt) -> c14(A__PLUS(tt, a__U51(mark(x0), x1, x2))) A__U52(tt, U51(x0, x1, x2), 0) -> c14(A__PLUS(0, a__U51(mark(x0), x1, x2))) A__U52(tt, U52(U11(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U52(tt, U52(U12(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U52(isNat(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__isNat(z0), x1, x2)), MARK(x3)) A__U52(tt, U52(U21(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U52(U31(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U52(tt, U52(U32(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U32(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U52(U41(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U41(mark(z0), z1), x1, x2)), MARK(x3)) A__U52(tt, U52(U51(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U51(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U52(U52(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U52(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U52(plus(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U52(tt, U52(U61(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U61(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U52(U71(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U71(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U52(U72(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U72(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U52(x(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U52(tt, U52(tt, x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(tt, x1, x2)), MARK(x3)) A__U52(tt, U52(s(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(s(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U52(0, x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(0, x1, x2)), MARK(x3)) A__U52(tt, U52(x0, x1, x2), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U52(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U52(tt, U52(x0, x1, x2), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U52(mark(x0), x1, x2)), MARK(U12(z0))) A__U52(tt, U52(x0, x1, x2), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U52(mark(x0), x1, x2)), MARK(isNat(z0))) A__U52(tt, U52(x0, x1, x2), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U52(mark(x0), x1, x2)), MARK(U21(z0))) A__U52(tt, U52(x0, x1, x2), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U52(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U52(tt, U52(x0, x1, x2), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U52(mark(x0), x1, x2)), MARK(U32(z0))) A__U52(tt, U52(x0, x1, x2), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U52(mark(x0), x1, x2)), MARK(U41(z0, z1))) A__U52(tt, U52(x0, x1, x2), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U52(mark(x0), x1, x2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(x0, x1, x2), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U52(mark(x0), x1, x2)), MARK(U52(z0, z1, z2))) A__U52(tt, U52(x0, x1, x2), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U52(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U52(tt, U52(x0, x1, x2), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U52(mark(x0), x1, x2)), MARK(U61(z0))) A__U52(tt, U52(x0, x1, x2), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U52(mark(x0), x1, x2)), MARK(U71(z0, z1, z2))) A__U52(tt, U52(x0, x1, x2), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U52(mark(x0), x1, x2)), MARK(U72(z0, z1, z2))) A__U52(tt, U52(x0, x1, x2), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U52(mark(x0), x1, x2)), MARK(x(z0, z1))) A__U52(tt, U52(x0, x1, x2), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U52(mark(x0), x1, x2)), MARK(s(z0))) A__U52(tt, U52(x0, z1, z2), x3) -> c14(MARK(x3)) A__U52(tt, U52(x0, x1, x2), tt) -> c14(A__PLUS(tt, a__U52(mark(x0), x1, x2))) A__U52(tt, U52(x0, x1, x2), 0) -> c14(A__PLUS(0, a__U52(mark(x0), x1, x2))) S tuples: A__U41(tt, z0) -> c10(MARK(z0)) MARK(isNat(z0)) -> c38(A__ISNAT(z0)) MARK(s(z0)) -> c53(MARK(z0)) A__U11(tt, z0) -> c(A__ISNAT(z0)) A__U31(tt, z0) -> c6(A__ISNAT(z0)) A__ISNAT(s(z0)) -> c27(A__ISNAT(z0)) A__X(z0, 0) -> c33(A__ISNAT(z0)) MARK(U12(z0)) -> c37(MARK(z0)) MARK(U21(z0)) -> c39(MARK(z0)) MARK(U32(z0)) -> c41(MARK(z0)) MARK(U61(z0)) -> c47(MARK(z0)) A__U51(tt, x0, 0) -> c12(A__U52(tt, x0, 0)) A__U51(tt, x0, z0) -> c12(A__ISNAT(z0)) A__U52(tt, plus(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, U61(z0), x1) -> c14(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(x1)) A__U52(tt, U71(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, U72(z0, z1, z2), x1) -> c14(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(x1)) A__U52(tt, x(z0, z1), x1) -> c14(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x1)) A__U52(tt, s(z0), x1) -> c14(A__PLUS(mark(x1), s(mark(z0))), MARK(x1)) A__U52(tt, 0, x1) -> c14(A__PLUS(mark(x1), 0), MARK(x1)) A__U52(tt, x0, U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(U11(z0, z1))) A__U52(tt, x0, U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(U12(z0))) A__U52(tt, x0, isNat(z0)) -> c14(A__PLUS(a__isNat(z0), mark(x0)), MARK(isNat(z0))) A__U52(tt, x0, U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(U21(z0))) A__U52(tt, x0, U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(U31(z0, z1))) A__U52(tt, x0, U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(U32(z0))) A__U52(tt, x0, U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(U41(z0, z1))) A__U52(tt, x0, U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, x0, U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, x0, plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(plus(z0, z1))) A__U52(tt, x0, U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(U61(z0))) A__U52(tt, x0, U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, x0, U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, x0, x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x(z0, z1))) A__U52(tt, x0, s(z0)) -> c14(A__PLUS(s(mark(z0)), mark(x0)), MARK(s(z0))) A__U52(tt, tt, x1) -> c14(MARK(x1)) A__U52(tt, x0, tt) -> c14(A__PLUS(tt, mark(x0))) A__U52(tt, x0, 0) -> c14(A__PLUS(0, mark(x0))) A__U52(tt, U11(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U52(tt, U12(z0), x1) -> c15(A__PLUS(mark(x1), a__U12(mark(z0))), MARK(U12(z0))) A__U52(tt, isNat(z0), x1) -> c15(A__PLUS(mark(x1), a__isNat(z0)), MARK(isNat(z0))) A__U52(tt, U21(z0), x1) -> c15(A__PLUS(mark(x1), a__U21(mark(z0))), MARK(U21(z0))) A__U52(tt, U31(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U52(tt, U32(z0), x1) -> c15(A__PLUS(mark(x1), a__U32(mark(z0))), MARK(U32(z0))) A__U52(tt, U41(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U52(tt, U51(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U52(tt, plus(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U52(tt, U61(z0), x1) -> c15(A__PLUS(mark(x1), a__U61(mark(z0))), MARK(U61(z0))) A__U52(tt, U71(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U52(tt, U72(z0, z1, z2), x1) -> c15(A__PLUS(mark(x1), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U52(tt, x(z0, z1), x1) -> c15(A__PLUS(mark(x1), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U52(tt, s(z0), x1) -> c15(A__PLUS(mark(x1), s(mark(z0))), MARK(s(z0))) A__U52(tt, x0, U11(z0, z1)) -> c15(A__PLUS(a__U11(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U12(z0)) -> c15(A__PLUS(a__U12(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, isNat(z0)) -> c15(A__PLUS(a__isNat(z0), mark(x0)), MARK(x0)) A__U52(tt, x0, U21(z0)) -> c15(A__PLUS(a__U21(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U31(z0, z1)) -> c15(A__PLUS(a__U31(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U32(z0)) -> c15(A__PLUS(a__U32(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U41(z0, z1)) -> c15(A__PLUS(a__U41(mark(z0), z1), mark(x0)), MARK(x0)) A__U52(tt, x0, U51(z0, z1, z2)) -> c15(A__PLUS(a__U51(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U52(z0, z1, z2)) -> c15(A__PLUS(a__U52(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, plus(z0, z1)) -> c15(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, U61(z0)) -> c15(A__PLUS(a__U61(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, U71(z0, z1, z2)) -> c15(A__PLUS(a__U71(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, U72(z0, z1, z2)) -> c15(A__PLUS(a__U72(mark(z0), z1, z2), mark(x0)), MARK(x0)) A__U52(tt, x0, x(z0, z1)) -> c15(A__PLUS(a__x(mark(z0), mark(z1)), mark(x0)), MARK(x0)) A__U52(tt, x0, tt) -> c15(A__PLUS(tt, mark(x0)), MARK(x0)) A__U52(tt, x0, s(z0)) -> c15(A__PLUS(s(mark(z0)), mark(x0)), MARK(x0)) A__U52(tt, x0, 0) -> c15(A__PLUS(0, mark(x0)), MARK(x0)) A__U52(tt, 0, x1) -> c15(A__PLUS(mark(x1), 0)) A__U71(tt, x0, plus(z0, z1)) -> c19(A__U72(a__U11(a__isNat(z0), z1), x0, plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__U71(tt, x0, s(z0)) -> c19(A__U72(a__U21(a__isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U71(tt, x0, x(z0, z1)) -> c19(A__U72(a__U31(a__isNat(z0), z1), x0, x(z0, z1)), A__ISNAT(x(z0, z1))) A__U71(tt, x0, 0) -> c19(A__U72(tt, x0, 0)) A__U71(tt, x0, z0) -> c19(A__ISNAT(z0)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, x1) -> c21(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(x1)) A__U72(tt, U12(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(x1)) A__U72(tt, U21(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(x1)) A__U72(tt, U32(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(x1)) A__U72(tt, U61(z0), x1) -> c21(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c21(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c21(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x1)) A__U72(tt, tt, x1) -> c21(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt)), MARK(x1)) A__U72(tt, s(z0), x1) -> c21(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(x1)) A__U72(tt, 0, x1) -> c21(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c21(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c21(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c21(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c21(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c21(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c21(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c21(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c21(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c21(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c21(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c21(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c21(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(s(z0))) A__U72(tt, x0, tt) -> c21(A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0))) A__U72(tt, x0, tt) -> c21(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0))) A__U72(tt, x0, 0) -> c21(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(mark(0), mark(x0)), 0), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, x1) -> c22(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), A__X(mark(x1), mark(x0)), MARK(x0)) A__U72(tt, U11(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, U12(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), A__X(mark(x1), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, isNat(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), A__X(mark(x1), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, U21(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), A__X(mark(x1), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, U31(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, U32(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), A__X(mark(x1), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, U41(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), A__X(mark(x1), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, U51(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, U52(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, plus(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, U61(z0), x1) -> c22(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), A__X(mark(x1), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, U71(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, U72(z0, z1, z2), x1) -> c22(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), A__X(mark(x1), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x(z0, z1), x1) -> c22(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), A__X(mark(x1), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, s(z0), x1) -> c22(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), A__X(mark(x1), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, U11(z0, z1)) -> c22(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), A__X(mark(U11(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U12(z0)) -> c22(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), A__X(mark(U12(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, isNat(z0)) -> c22(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), A__X(mark(isNat(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U21(z0)) -> c22(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), A__X(mark(U21(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U31(z0, z1)) -> c22(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), A__X(mark(U31(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U32(z0)) -> c22(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), A__X(mark(U32(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U41(z0, z1)) -> c22(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), A__X(mark(U41(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U51(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), A__X(mark(U51(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U52(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), A__X(mark(U52(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, plus(z0, z1)) -> c22(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), A__X(mark(plus(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, U61(z0)) -> c22(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), A__X(mark(U61(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, U71(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), A__X(mark(U71(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, U72(z0, z1, z2)) -> c22(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), A__X(mark(U72(z0, z1, z2)), mark(x0)), MARK(x0)) A__U72(tt, x0, x(z0, z1)) -> c22(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), A__X(mark(x(z0, z1)), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__PLUS(a__x(tt, mark(x0)), mark(tt)), A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, x0, s(z0)) -> c22(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), A__X(mark(s(z0)), mark(x0)), MARK(x0)) A__U72(tt, x0, 0) -> c22(A__PLUS(a__x(0, mark(x0)), mark(0)), A__X(mark(0), mark(x0)), MARK(x0)) A__U72(tt, x0, tt) -> c22(A__X(mark(tt), mark(x0)), MARK(x0)) A__U72(tt, tt, x1) -> c22(A__PLUS(a__x(mark(x1), tt), mark(x1)), A__X(mark(x1), mark(tt))) A__U72(tt, 0, x1) -> c22(A__PLUS(a__x(mark(x1), 0), mark(x1)), A__X(mark(x1), mark(0))) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(mark(U11(z0, z1)), mark(x0)), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(mark(U12(z0)), mark(x0)), a__U12(mark(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(mark(isNat(z0)), mark(x0)), a__isNat(z0)), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(mark(U21(z0)), mark(x0)), a__U21(mark(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(mark(U31(z0, z1)), mark(x0)), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(mark(U32(z0)), mark(x0)), a__U32(mark(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(mark(U41(z0, z1)), mark(x0)), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U51(z0, z1, z2)), mark(x0)), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U52(z0, z1, z2)), mark(x0)), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(mark(plus(z0, z1)), mark(x0)), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(mark(U61(z0)), mark(x0)), a__U61(mark(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U71(z0, z1, z2)), mark(x0)), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(mark(U72(z0, z1, z2)), mark(x0)), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(mark(x(z0, z1)), mark(x0)), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(mark(s(z0)), mark(x0)), s(mark(z0))), MARK(s(z0))) A__U72(tt, x0, x1) -> c23(A__PLUS(x(mark(x1), mark(x0)), mark(x1)), MARK(x1)) A__U72(tt, U11(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U11(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U12(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U12(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, isNat(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__isNat(z0)), mark(x1)), MARK(x1)) A__U72(tt, U21(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U21(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U31(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U31(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U32(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U32(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U41(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__U41(mark(z0), z1)), mark(x1)), MARK(x1)) A__U72(tt, U51(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U51(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U52(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U52(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, plus(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__plus(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, U61(z0), x1) -> c23(A__PLUS(a__x(mark(x1), a__U61(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, U71(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U71(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, U72(z0, z1, z2), x1) -> c23(A__PLUS(a__x(mark(x1), a__U72(mark(z0), z1, z2)), mark(x1)), MARK(x1)) A__U72(tt, x(z0, z1), x1) -> c23(A__PLUS(a__x(mark(x1), a__x(mark(z0), mark(z1))), mark(x1)), MARK(x1)) A__U72(tt, tt, x1) -> c23(A__PLUS(a__x(mark(x1), tt), mark(x1)), MARK(x1)) A__U72(tt, s(z0), x1) -> c23(A__PLUS(a__x(mark(x1), s(mark(z0))), mark(x1)), MARK(x1)) A__U72(tt, 0, x1) -> c23(A__PLUS(a__x(mark(x1), 0), mark(x1)), MARK(x1)) A__U72(tt, x0, U11(z0, z1)) -> c23(A__PLUS(a__x(a__U11(mark(z0), z1), mark(x0)), mark(U11(z0, z1))), MARK(U11(z0, z1))) A__U72(tt, x0, U12(z0)) -> c23(A__PLUS(a__x(a__U12(mark(z0)), mark(x0)), mark(U12(z0))), MARK(U12(z0))) A__U72(tt, x0, isNat(z0)) -> c23(A__PLUS(a__x(a__isNat(z0), mark(x0)), mark(isNat(z0))), MARK(isNat(z0))) A__U72(tt, x0, U21(z0)) -> c23(A__PLUS(a__x(a__U21(mark(z0)), mark(x0)), mark(U21(z0))), MARK(U21(z0))) A__U72(tt, x0, U31(z0, z1)) -> c23(A__PLUS(a__x(a__U31(mark(z0), z1), mark(x0)), mark(U31(z0, z1))), MARK(U31(z0, z1))) A__U72(tt, x0, U32(z0)) -> c23(A__PLUS(a__x(a__U32(mark(z0)), mark(x0)), mark(U32(z0))), MARK(U32(z0))) A__U72(tt, x0, U41(z0, z1)) -> c23(A__PLUS(a__x(a__U41(mark(z0), z1), mark(x0)), mark(U41(z0, z1))), MARK(U41(z0, z1))) A__U72(tt, x0, U51(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U51(mark(z0), z1, z2), mark(x0)), mark(U51(z0, z1, z2))), MARK(U51(z0, z1, z2))) A__U72(tt, x0, U52(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U52(mark(z0), z1, z2), mark(x0)), mark(U52(z0, z1, z2))), MARK(U52(z0, z1, z2))) A__U72(tt, x0, plus(z0, z1)) -> c23(A__PLUS(a__x(a__plus(mark(z0), mark(z1)), mark(x0)), mark(plus(z0, z1))), MARK(plus(z0, z1))) A__U72(tt, x0, U61(z0)) -> c23(A__PLUS(a__x(a__U61(mark(z0)), mark(x0)), mark(U61(z0))), MARK(U61(z0))) A__U72(tt, x0, U71(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U71(mark(z0), z1, z2), mark(x0)), mark(U71(z0, z1, z2))), MARK(U71(z0, z1, z2))) A__U72(tt, x0, U72(z0, z1, z2)) -> c23(A__PLUS(a__x(a__U72(mark(z0), z1, z2), mark(x0)), mark(U72(z0, z1, z2))), MARK(U72(z0, z1, z2))) A__U72(tt, x0, x(z0, z1)) -> c23(A__PLUS(a__x(a__x(mark(z0), mark(z1)), mark(x0)), mark(x(z0, z1))), MARK(x(z0, z1))) A__U72(tt, x0, s(z0)) -> c23(A__PLUS(a__x(s(mark(z0)), mark(x0)), mark(s(z0))), MARK(s(z0))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(mark(0), mark(x0)), 0)) A__U72(tt, x0, tt) -> c23(A__PLUS(a__x(tt, mark(x0)), mark(tt))) A__U72(tt, x0, 0) -> c23(A__PLUS(a__x(0, mark(x0)), mark(0))) A__ISNAT(plus(plus(z0, z1), x1)) -> c26(A__U11(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(plus(s(z0), x1)) -> c26(A__U11(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(plus(x(z0, z1), x1)) -> c26(A__U11(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(plus(0, x1)) -> c26(A__U11(tt, x1)) A__ISNAT(plus(z0, x1)) -> c26(A__ISNAT(z0)) A__ISNAT(x(plus(z0, z1), x1)) -> c28(A__U31(a__U11(a__isNat(z0), z1), x1), A__ISNAT(plus(z0, z1))) A__ISNAT(x(s(z0), x1)) -> c28(A__U31(a__U21(a__isNat(z0)), x1), A__ISNAT(s(z0))) A__ISNAT(x(x(z0, z1), x1)) -> c28(A__U31(a__U31(a__isNat(z0), z1), x1), A__ISNAT(x(z0, z1))) A__ISNAT(x(0, x1)) -> c28(A__U31(tt, x1)) A__ISNAT(x(z0, x1)) -> c28(A__ISNAT(z0)) A__PLUS(plus(z0, z1), 0) -> c30(A__U41(a__U11(a__isNat(z0), z1), plus(z0, z1)), A__ISNAT(plus(z0, z1))) A__PLUS(s(z0), 0) -> c30(A__U41(a__U21(a__isNat(z0)), s(z0)), A__ISNAT(s(z0))) A__PLUS(x(z0, z1), 0) -> c30(A__U41(a__U31(a__isNat(z0), z1), x(z0, z1)), A__ISNAT(x(z0, z1))) A__PLUS(0, 0) -> c30(A__U41(tt, 0)) A__PLUS(z0, 0) -> c30(A__ISNAT(z0)) A__PLUS(x0, s(plus(z0, z1))) -> c31(A__U51(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__PLUS(x0, s(s(z0))) -> c31(A__U51(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__PLUS(x0, s(x(z0, z1))) -> c31(A__U51(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__PLUS(x0, s(0)) -> c31(A__U51(tt, 0, x0)) A__PLUS(x0, s(z0)) -> c31(A__ISNAT(z0)) A__X(x0, s(plus(z0, z1))) -> c34(A__U71(a__U11(a__isNat(z0), z1), plus(z0, z1), x0), A__ISNAT(plus(z0, z1))) A__X(x0, s(s(z0))) -> c34(A__U71(a__U21(a__isNat(z0)), s(z0), x0), A__ISNAT(s(z0))) A__X(x0, s(x(z0, z1))) -> c34(A__U71(a__U31(a__isNat(z0), z1), x(z0, z1), x0), A__ISNAT(x(z0, z1))) A__X(x0, s(0)) -> c34(A__U71(tt, 0, x0)) A__X(x0, s(z0)) -> c34(A__ISNAT(z0)) MARK(U11(U11(z0, z1), x1)) -> c36(A__U11(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U11(U12(z0), x1)) -> c36(A__U11(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U11(U21(z0), x1)) -> c36(A__U11(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U11(U31(z0, z1), x1)) -> c36(A__U11(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U11(U32(z0), x1)) -> c36(A__U11(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U11(U41(z0, z1), x1)) -> c36(A__U11(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U11(U51(z0, z1, z2), x1)) -> c36(A__U11(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U11(U52(z0, z1, z2), x1)) -> c36(A__U11(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U11(plus(z0, z1), x1)) -> c36(A__U11(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U11(U61(z0), x1)) -> c36(A__U11(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U11(U71(z0, z1, z2), x1)) -> c36(A__U11(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U11(U72(z0, z1, z2), x1)) -> c36(A__U11(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U11(x(z0, z1), x1)) -> c36(A__U11(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U11(tt, x1)) -> c36(A__U11(tt, x1)) MARK(U11(s(z0), x1)) -> c36(MARK(s(z0))) MARK(U11(isNat(z0), x1)) -> c1(A__U11(a__isNat(z0), x1)) MARK(U11(isNat(z0), x1)) -> c1(MARK(isNat(z0))) MARK(U31(U11(z0, z1), x1)) -> c40(A__U31(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U31(U12(z0), x1)) -> c40(A__U31(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U31(U21(z0), x1)) -> c40(A__U31(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U31(U31(z0, z1), x1)) -> c40(A__U31(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U31(U32(z0), x1)) -> c40(A__U31(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U31(U41(z0, z1), x1)) -> c40(A__U31(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U31(U51(z0, z1, z2), x1)) -> c40(A__U31(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U31(U52(z0, z1, z2), x1)) -> c40(A__U31(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U31(plus(z0, z1), x1)) -> c40(A__U31(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U31(U61(z0), x1)) -> c40(A__U31(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U31(U71(z0, z1, z2), x1)) -> c40(A__U31(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U31(U72(z0, z1, z2), x1)) -> c40(A__U31(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U31(x(z0, z1), x1)) -> c40(A__U31(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U31(tt, x1)) -> c40(A__U31(tt, x1)) MARK(U31(s(z0), x1)) -> c40(MARK(s(z0))) MARK(U31(isNat(z0), x1)) -> c2(A__U31(a__isNat(z0), x1)) MARK(U31(isNat(z0), x1)) -> c2(MARK(isNat(z0))) MARK(U41(U11(z0, z1), x1)) -> c42(A__U41(a__U11(mark(z0), z1), x1), MARK(U11(z0, z1))) MARK(U41(U12(z0), x1)) -> c42(A__U41(a__U12(mark(z0)), x1), MARK(U12(z0))) MARK(U41(isNat(z0), x1)) -> c42(A__U41(a__isNat(z0), x1), MARK(isNat(z0))) MARK(U41(U21(z0), x1)) -> c42(A__U41(a__U21(mark(z0)), x1), MARK(U21(z0))) MARK(U41(U31(z0, z1), x1)) -> c42(A__U41(a__U31(mark(z0), z1), x1), MARK(U31(z0, z1))) MARK(U41(U32(z0), x1)) -> c42(A__U41(a__U32(mark(z0)), x1), MARK(U32(z0))) MARK(U41(U41(z0, z1), x1)) -> c42(A__U41(a__U41(mark(z0), z1), x1), MARK(U41(z0, z1))) MARK(U41(U51(z0, z1, z2), x1)) -> c42(A__U41(a__U51(mark(z0), z1, z2), x1), MARK(U51(z0, z1, z2))) MARK(U41(U52(z0, z1, z2), x1)) -> c42(A__U41(a__U52(mark(z0), z1, z2), x1), MARK(U52(z0, z1, z2))) MARK(U41(plus(z0, z1), x1)) -> c42(A__U41(a__plus(mark(z0), mark(z1)), x1), MARK(plus(z0, z1))) MARK(U41(U61(z0), x1)) -> c42(A__U41(a__U61(mark(z0)), x1), MARK(U61(z0))) MARK(U41(U71(z0, z1, z2), x1)) -> c42(A__U41(a__U71(mark(z0), z1, z2), x1), MARK(U71(z0, z1, z2))) MARK(U41(U72(z0, z1, z2), x1)) -> c42(A__U41(a__U72(mark(z0), z1, z2), x1), MARK(U72(z0, z1, z2))) MARK(U41(x(z0, z1), x1)) -> c42(A__U41(a__x(mark(z0), mark(z1)), x1), MARK(x(z0, z1))) MARK(U41(tt, x1)) -> c42(A__U41(tt, x1)) MARK(U41(s(z0), x1)) -> c42(MARK(s(z0))) MARK(U51(U11(z0, z1), x1, x2)) -> c43(A__U51(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U51(U12(z0), x1, x2)) -> c43(A__U51(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U51(isNat(z0), x1, x2)) -> c43(A__U51(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U51(U21(z0), x1, x2)) -> c43(A__U51(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U51(U31(z0, z1), x1, x2)) -> c43(A__U51(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U51(U32(z0), x1, x2)) -> c43(A__U51(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U51(U41(z0, z1), x1, x2)) -> c43(A__U51(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U51(U51(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U51(U52(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U51(plus(z0, z1), x1, x2)) -> c43(A__U51(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U51(U61(z0), x1, x2)) -> c43(A__U51(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U51(U71(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U51(U72(z0, z1, z2), x1, x2)) -> c43(A__U51(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U51(x(z0, z1), x1, x2)) -> c43(A__U51(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U51(tt, x1, x2)) -> c43(A__U51(tt, x1, x2)) MARK(U51(s(z0), x1, x2)) -> c43(MARK(s(z0))) MARK(U52(U11(z0, z1), x1, x2)) -> c44(A__U52(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U52(U12(z0), x1, x2)) -> c44(A__U52(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U52(isNat(z0), x1, x2)) -> c44(A__U52(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U52(U21(z0), x1, x2)) -> c44(A__U52(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U52(U31(z0, z1), x1, x2)) -> c44(A__U52(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U52(U32(z0), x1, x2)) -> c44(A__U52(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U52(U41(z0, z1), x1, x2)) -> c44(A__U52(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U52(U51(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U52(U52(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U52(plus(z0, z1), x1, x2)) -> c44(A__U52(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U52(U61(z0), x1, x2)) -> c44(A__U52(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U52(U71(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U52(U72(z0, z1, z2), x1, x2)) -> c44(A__U52(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U52(x(z0, z1), x1, x2)) -> c44(A__U52(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U52(tt, x1, x2)) -> c44(A__U52(tt, x1, x2)) MARK(U52(s(z0), x1, x2)) -> c44(MARK(s(z0))) MARK(plus(x0, U11(z0, z1))) -> c45(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U12(z0))) -> c45(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(plus(x0, isNat(z0))) -> c45(A__PLUS(mark(x0), a__isNat(z0)), MARK(x0)) MARK(plus(x0, U21(z0))) -> c45(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(plus(x0, U31(z0, z1))) -> c45(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U32(z0))) -> c45(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(plus(x0, U41(z0, z1))) -> c45(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(plus(x0, U51(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U52(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, plus(z0, z1))) -> c45(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, U61(z0))) -> c45(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(plus(x0, U71(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, U72(z0, z1, z2))) -> c45(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(plus(x0, x(z0, z1))) -> c45(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(plus(x0, s(z0))) -> c45(A__PLUS(mark(x0), s(mark(z0))), MARK(x0)) MARK(plus(x0, 0)) -> c45(A__PLUS(mark(x0), 0), MARK(x0)) MARK(plus(U11(z0, z1), x1)) -> c45(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(plus(U12(z0), x1)) -> c45(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(plus(isNat(z0), x1)) -> c45(A__PLUS(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(plus(U21(z0), x1)) -> c45(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(plus(U31(z0, z1), x1)) -> c45(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(plus(U32(z0), x1)) -> c45(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(plus(U41(z0, z1), x1)) -> c45(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(plus(U51(z0, z1, z2), x1)) -> c45(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(plus(U52(z0, z1, z2), x1)) -> c45(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(plus(plus(z0, z1), x1)) -> c45(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(plus(U61(z0), x1)) -> c45(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(plus(U71(z0, z1, z2), x1)) -> c45(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(plus(U72(z0, z1, z2), x1)) -> c45(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(plus(x(z0, z1), x1)) -> c45(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(plus(s(z0), x1)) -> c45(A__PLUS(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(plus(x0, tt)) -> c45(MARK(x0)) MARK(plus(tt, x1)) -> c45(A__PLUS(tt, mark(x1))) MARK(plus(0, x1)) -> c45(A__PLUS(0, mark(x1))) MARK(plus(x0, U11(z0, z1))) -> c46(A__PLUS(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(plus(x0, U12(z0))) -> c46(A__PLUS(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(plus(x0, isNat(z0))) -> c46(A__PLUS(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(plus(x0, U21(z0))) -> c46(A__PLUS(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(plus(x0, U31(z0, z1))) -> c46(A__PLUS(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(plus(x0, U32(z0))) -> c46(A__PLUS(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(plus(x0, U41(z0, z1))) -> c46(A__PLUS(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(plus(x0, U51(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(plus(x0, U52(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(plus(x0, plus(z0, z1))) -> c46(A__PLUS(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(plus(x0, U61(z0))) -> c46(A__PLUS(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(plus(x0, U71(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(plus(x0, U72(z0, z1, z2))) -> c46(A__PLUS(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(plus(x0, x(z0, z1))) -> c46(A__PLUS(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(plus(x0, s(z0))) -> c46(A__PLUS(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(plus(U11(z0, z1), x1)) -> c46(A__PLUS(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U12(z0), x1)) -> c46(A__PLUS(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(isNat(z0), x1)) -> c46(A__PLUS(a__isNat(z0), mark(x1)), MARK(x1)) MARK(plus(U21(z0), x1)) -> c46(A__PLUS(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U31(z0, z1), x1)) -> c46(A__PLUS(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U32(z0), x1)) -> c46(A__PLUS(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U41(z0, z1), x1)) -> c46(A__PLUS(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(plus(U51(z0, z1, z2), x1)) -> c46(A__PLUS(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U52(z0, z1, z2), x1)) -> c46(A__PLUS(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(plus(z0, z1), x1)) -> c46(A__PLUS(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(U61(z0), x1)) -> c46(A__PLUS(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(U71(z0, z1, z2), x1)) -> c46(A__PLUS(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(U72(z0, z1, z2), x1)) -> c46(A__PLUS(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(plus(x(z0, z1), x1)) -> c46(A__PLUS(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(plus(tt, x1)) -> c46(A__PLUS(tt, mark(x1)), MARK(x1)) MARK(plus(s(z0), x1)) -> c46(A__PLUS(s(mark(z0)), mark(x1)), MARK(x1)) MARK(plus(0, x1)) -> c46(A__PLUS(0, mark(x1)), MARK(x1)) MARK(plus(x0, 0)) -> c46(A__PLUS(mark(x0), 0)) MARK(U71(U11(z0, z1), x1, x2)) -> c48(A__U71(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U71(U12(z0), x1, x2)) -> c48(A__U71(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U71(isNat(z0), x1, x2)) -> c48(A__U71(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U71(U21(z0), x1, x2)) -> c48(A__U71(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U71(U31(z0, z1), x1, x2)) -> c48(A__U71(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U71(U32(z0), x1, x2)) -> c48(A__U71(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U71(U41(z0, z1), x1, x2)) -> c48(A__U71(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U71(U51(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U71(U52(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U71(plus(z0, z1), x1, x2)) -> c48(A__U71(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U71(U61(z0), x1, x2)) -> c48(A__U71(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U71(U71(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U71(U72(z0, z1, z2), x1, x2)) -> c48(A__U71(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U71(x(z0, z1), x1, x2)) -> c48(A__U71(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U71(tt, x1, x2)) -> c48(A__U71(tt, x1, x2)) MARK(U71(s(z0), x1, x2)) -> c48(MARK(s(z0))) MARK(U72(U11(z0, z1), x1, x2)) -> c49(A__U72(a__U11(mark(z0), z1), x1, x2), MARK(U11(z0, z1))) MARK(U72(U12(z0), x1, x2)) -> c49(A__U72(a__U12(mark(z0)), x1, x2), MARK(U12(z0))) MARK(U72(isNat(z0), x1, x2)) -> c49(A__U72(a__isNat(z0), x1, x2), MARK(isNat(z0))) MARK(U72(U21(z0), x1, x2)) -> c49(A__U72(a__U21(mark(z0)), x1, x2), MARK(U21(z0))) MARK(U72(U31(z0, z1), x1, x2)) -> c49(A__U72(a__U31(mark(z0), z1), x1, x2), MARK(U31(z0, z1))) MARK(U72(U32(z0), x1, x2)) -> c49(A__U72(a__U32(mark(z0)), x1, x2), MARK(U32(z0))) MARK(U72(U41(z0, z1), x1, x2)) -> c49(A__U72(a__U41(mark(z0), z1), x1, x2), MARK(U41(z0, z1))) MARK(U72(U51(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U51(mark(z0), z1, z2), x1, x2), MARK(U51(z0, z1, z2))) MARK(U72(U52(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U52(mark(z0), z1, z2), x1, x2), MARK(U52(z0, z1, z2))) MARK(U72(plus(z0, z1), x1, x2)) -> c49(A__U72(a__plus(mark(z0), mark(z1)), x1, x2), MARK(plus(z0, z1))) MARK(U72(U61(z0), x1, x2)) -> c49(A__U72(a__U61(mark(z0)), x1, x2), MARK(U61(z0))) MARK(U72(U71(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U71(mark(z0), z1, z2), x1, x2), MARK(U71(z0, z1, z2))) MARK(U72(U72(z0, z1, z2), x1, x2)) -> c49(A__U72(a__U72(mark(z0), z1, z2), x1, x2), MARK(U72(z0, z1, z2))) MARK(U72(x(z0, z1), x1, x2)) -> c49(A__U72(a__x(mark(z0), mark(z1)), x1, x2), MARK(x(z0, z1))) MARK(U72(tt, x1, x2)) -> c49(A__U72(tt, x1, x2)) MARK(U72(s(z0), x1, x2)) -> c49(MARK(s(z0))) MARK(x(x0, U11(z0, z1))) -> c50(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(x0)) MARK(x(x0, U12(z0))) -> c50(A__X(mark(x0), a__U12(mark(z0))), MARK(x0)) MARK(x(x0, isNat(z0))) -> c50(A__X(mark(x0), a__isNat(z0)), MARK(x0)) MARK(x(x0, U21(z0))) -> c50(A__X(mark(x0), a__U21(mark(z0))), MARK(x0)) MARK(x(x0, U31(z0, z1))) -> c50(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(x0)) MARK(x(x0, U32(z0))) -> c50(A__X(mark(x0), a__U32(mark(z0))), MARK(x0)) MARK(x(x0, U41(z0, z1))) -> c50(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(x0)) MARK(x(x0, U51(z0, z1, z2))) -> c50(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U52(z0, z1, z2))) -> c50(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, plus(z0, z1))) -> c50(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, U61(z0))) -> c50(A__X(mark(x0), a__U61(mark(z0))), MARK(x0)) MARK(x(x0, U71(z0, z1, z2))) -> c50(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, U72(z0, z1, z2))) -> c50(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(x0)) MARK(x(x0, x(z0, z1))) -> c50(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x0)) MARK(x(x0, s(z0))) -> c50(A__X(mark(x0), s(mark(z0))), MARK(x0)) MARK(x(x0, 0)) -> c50(A__X(mark(x0), 0), MARK(x0)) MARK(x(U11(z0, z1), x1)) -> c50(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(U11(z0, z1))) MARK(x(U12(z0), x1)) -> c50(A__X(a__U12(mark(z0)), mark(x1)), MARK(U12(z0))) MARK(x(isNat(z0), x1)) -> c50(A__X(a__isNat(z0), mark(x1)), MARK(isNat(z0))) MARK(x(U21(z0), x1)) -> c50(A__X(a__U21(mark(z0)), mark(x1)), MARK(U21(z0))) MARK(x(U31(z0, z1), x1)) -> c50(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(U31(z0, z1))) MARK(x(U32(z0), x1)) -> c50(A__X(a__U32(mark(z0)), mark(x1)), MARK(U32(z0))) MARK(x(U41(z0, z1), x1)) -> c50(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(U41(z0, z1))) MARK(x(U51(z0, z1, z2), x1)) -> c50(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(U51(z0, z1, z2))) MARK(x(U52(z0, z1, z2), x1)) -> c50(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(U52(z0, z1, z2))) MARK(x(plus(z0, z1), x1)) -> c50(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(plus(z0, z1))) MARK(x(U61(z0), x1)) -> c50(A__X(a__U61(mark(z0)), mark(x1)), MARK(U61(z0))) MARK(x(U71(z0, z1, z2), x1)) -> c50(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(U71(z0, z1, z2))) MARK(x(U72(z0, z1, z2), x1)) -> c50(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(U72(z0, z1, z2))) MARK(x(x(z0, z1), x1)) -> c50(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x(z0, z1))) MARK(x(s(z0), x1)) -> c50(A__X(s(mark(z0)), mark(x1)), MARK(s(z0))) MARK(x(x0, tt)) -> c50(MARK(x0)) MARK(x(tt, x1)) -> c50(A__X(tt, mark(x1))) MARK(x(0, x1)) -> c50(A__X(0, mark(x1))) MARK(x(x0, U11(z0, z1))) -> c51(A__X(mark(x0), a__U11(mark(z0), z1)), MARK(U11(z0, z1))) MARK(x(x0, U12(z0))) -> c51(A__X(mark(x0), a__U12(mark(z0))), MARK(U12(z0))) MARK(x(x0, isNat(z0))) -> c51(A__X(mark(x0), a__isNat(z0)), MARK(isNat(z0))) MARK(x(x0, U21(z0))) -> c51(A__X(mark(x0), a__U21(mark(z0))), MARK(U21(z0))) MARK(x(x0, U31(z0, z1))) -> c51(A__X(mark(x0), a__U31(mark(z0), z1)), MARK(U31(z0, z1))) MARK(x(x0, U32(z0))) -> c51(A__X(mark(x0), a__U32(mark(z0))), MARK(U32(z0))) MARK(x(x0, U41(z0, z1))) -> c51(A__X(mark(x0), a__U41(mark(z0), z1)), MARK(U41(z0, z1))) MARK(x(x0, U51(z0, z1, z2))) -> c51(A__X(mark(x0), a__U51(mark(z0), z1, z2)), MARK(U51(z0, z1, z2))) MARK(x(x0, U52(z0, z1, z2))) -> c51(A__X(mark(x0), a__U52(mark(z0), z1, z2)), MARK(U52(z0, z1, z2))) MARK(x(x0, plus(z0, z1))) -> c51(A__X(mark(x0), a__plus(mark(z0), mark(z1))), MARK(plus(z0, z1))) MARK(x(x0, U61(z0))) -> c51(A__X(mark(x0), a__U61(mark(z0))), MARK(U61(z0))) MARK(x(x0, U71(z0, z1, z2))) -> c51(A__X(mark(x0), a__U71(mark(z0), z1, z2)), MARK(U71(z0, z1, z2))) MARK(x(x0, U72(z0, z1, z2))) -> c51(A__X(mark(x0), a__U72(mark(z0), z1, z2)), MARK(U72(z0, z1, z2))) MARK(x(x0, x(z0, z1))) -> c51(A__X(mark(x0), a__x(mark(z0), mark(z1))), MARK(x(z0, z1))) MARK(x(x0, s(z0))) -> c51(A__X(mark(x0), s(mark(z0))), MARK(s(z0))) MARK(x(U11(z0, z1), x1)) -> c51(A__X(a__U11(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U12(z0), x1)) -> c51(A__X(a__U12(mark(z0)), mark(x1)), MARK(x1)) MARK(x(isNat(z0), x1)) -> c51(A__X(a__isNat(z0), mark(x1)), MARK(x1)) MARK(x(U21(z0), x1)) -> c51(A__X(a__U21(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U31(z0, z1), x1)) -> c51(A__X(a__U31(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U32(z0), x1)) -> c51(A__X(a__U32(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U41(z0, z1), x1)) -> c51(A__X(a__U41(mark(z0), z1), mark(x1)), MARK(x1)) MARK(x(U51(z0, z1, z2), x1)) -> c51(A__X(a__U51(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U52(z0, z1, z2), x1)) -> c51(A__X(a__U52(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(plus(z0, z1), x1)) -> c51(A__X(a__plus(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(U61(z0), x1)) -> c51(A__X(a__U61(mark(z0)), mark(x1)), MARK(x1)) MARK(x(U71(z0, z1, z2), x1)) -> c51(A__X(a__U71(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(U72(z0, z1, z2), x1)) -> c51(A__X(a__U72(mark(z0), z1, z2), mark(x1)), MARK(x1)) MARK(x(x(z0, z1), x1)) -> c51(A__X(a__x(mark(z0), mark(z1)), mark(x1)), MARK(x1)) MARK(x(tt, x1)) -> c51(A__X(tt, mark(x1)), MARK(x1)) MARK(x(s(z0), x1)) -> c51(A__X(s(mark(z0)), mark(x1)), MARK(x1)) MARK(x(0, x1)) -> c51(A__X(0, mark(x1)), MARK(x1)) MARK(x(x0, 0)) -> c51(A__X(mark(x0), 0)) A__U51(tt, x0, plus(0, x2)) -> c12(A__U52(a__U11(tt, x2), x0, plus(0, x2)), A__ISNAT(plus(0, x2))) A__U51(tt, x0, plus(plus(z0, z1), x2)) -> c12(A__U52(a__U11(a__U11(a__isNat(z0), z1), x2), x0, plus(plus(z0, z1), x2)), A__ISNAT(plus(plus(z0, z1), x2))) A__U51(tt, x0, plus(s(z0), x2)) -> c12(A__U52(a__U11(a__U21(a__isNat(z0)), x2), x0, plus(s(z0), x2)), A__ISNAT(plus(s(z0), x2))) A__U51(tt, x0, plus(x(z0, z1), x2)) -> c12(A__U52(a__U11(a__U31(a__isNat(z0), z1), x2), x0, plus(x(z0, z1), x2)), A__ISNAT(plus(x(z0, z1), x2))) A__U51(tt, x0, plus(z0, x2)) -> c12(A__U52(a__U11(isNat(z0), x2), x0, plus(z0, x2)), A__ISNAT(plus(z0, x2))) A__U51(tt, x0, plus(x1, z1)) -> c12(A__ISNAT(plus(x1, z1))) A__U51(tt, x0, s(0)) -> c12(A__U52(a__U21(tt), x0, s(0)), A__ISNAT(s(0))) A__U51(tt, x0, s(plus(z0, z1))) -> c12(A__U52(a__U21(a__U11(a__isNat(z0), z1)), x0, s(plus(z0, z1))), A__ISNAT(s(plus(z0, z1)))) A__U51(tt, x0, s(s(z0))) -> c12(A__U52(a__U21(a__U21(a__isNat(z0))), x0, s(s(z0))), A__ISNAT(s(s(z0)))) A__U51(tt, x0, s(x(z0, z1))) -> c12(A__U52(a__U21(a__U31(a__isNat(z0), z1)), x0, s(x(z0, z1))), A__ISNAT(s(x(z0, z1)))) A__U51(tt, x0, s(z0)) -> c12(A__U52(a__U21(isNat(z0)), x0, s(z0)), A__ISNAT(s(z0))) A__U51(tt, x0, s(x1)) -> c12(A__ISNAT(s(x1))) A__U51(tt, x0, x(0, x2)) -> c12(A__U52(a__U31(tt, x2), x0, x(0, x2)), A__ISNAT(x(0, x2))) A__U51(tt, x0, x(plus(z0, z1), x2)) -> c12(A__U52(a__U31(a__U11(a__isNat(z0), z1), x2), x0, x(plus(z0, z1), x2)), A__ISNAT(x(plus(z0, z1), x2))) A__U51(tt, x0, x(s(z0), x2)) -> c12(A__U52(a__U31(a__U21(a__isNat(z0)), x2), x0, x(s(z0), x2)), A__ISNAT(x(s(z0), x2))) A__U51(tt, x0, x(x(z0, z1), x2)) -> c12(A__U52(a__U31(a__U31(a__isNat(z0), z1), x2), x0, x(x(z0, z1), x2)), A__ISNAT(x(x(z0, z1), x2))) A__U51(tt, x0, x(z0, x2)) -> c12(A__U52(a__U31(isNat(z0), x2), x0, x(z0, x2)), A__ISNAT(x(z0, x2))) A__U51(tt, x0, x(x1, z1)) -> c12(A__ISNAT(x(x1, z1))) A__U52(tt, U11(U11(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U11(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U12(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U12(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(isNat(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__isNat(z0), x1)), MARK(x2)) A__U52(tt, U11(U21(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U21(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U31(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U31(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U32(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U32(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U41(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U41(mark(z0), z1), x1)), MARK(x2)) A__U52(tt, U11(U51(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U51(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U52(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U52(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(plus(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__plus(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(U61(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U61(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(U71(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U71(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(U72(z0, z1, z2), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__U72(mark(z0), z1, z2), x1)), MARK(x2)) A__U52(tt, U11(x(z0, z1), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(a__x(mark(z0), mark(z1)), x1)), MARK(x2)) A__U52(tt, U11(tt, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(tt, x1)), MARK(x2)) A__U52(tt, U11(s(z0), x1), x2) -> c14(A__PLUS(mark(x2), a__U11(s(mark(z0)), x1)), MARK(x2)) A__U52(tt, U11(0, x1), x2) -> c14(A__PLUS(mark(x2), a__U11(0, x1)), MARK(x2)) A__U52(tt, U11(x0, x1), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U11(z0, z1))) A__U52(tt, U11(x0, x1), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U11(mark(x0), x1)), MARK(U12(z0))) A__U52(tt, U11(x0, x1), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U11(mark(x0), x1)), MARK(isNat(z0))) A__U52(tt, U11(x0, x1), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U11(mark(x0), x1)), MARK(U21(z0))) A__U52(tt, U11(x0, x1), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U11(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U11(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U11(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U11(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U11(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U11(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U11(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U11(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U11(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U11(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U11(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U11(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U11(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U11(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U11(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U11(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U11(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U11(x0, x1), tt) -> c14(A__PLUS(tt, a__U11(mark(x0), x1))) A__U52(tt, U11(x0, x1), 0) -> c14(A__PLUS(0, a__U11(mark(x0), x1))) A__U52(tt, U12(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U12(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__isNat(z0))), MARK(x1)) A__U52(tt, U12(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U12(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U12(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U12(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U12(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U12(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U12(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U12(tt), x1) -> c14(A__PLUS(mark(x1), a__U12(tt)), MARK(x1)) A__U52(tt, U12(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U12(s(mark(z0)))), MARK(x1)) A__U52(tt, U12(0), x1) -> c14(A__PLUS(mark(x1), a__U12(0)), MARK(x1)) A__U52(tt, U12(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U12(mark(x0))), MARK(U11(z0, z1))) A__U52(tt, U12(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U12(mark(x0))), MARK(U12(z0))) A__U52(tt, U12(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U12(mark(x0))), MARK(isNat(z0))) A__U52(tt, U12(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U12(mark(x0))), MARK(U21(z0))) A__U52(tt, U12(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U12(mark(x0))), MARK(U31(z0, z1))) A__U52(tt, U12(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U12(mark(x0))), MARK(U32(z0))) A__U52(tt, U12(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U12(mark(x0))), MARK(U41(z0, z1))) A__U52(tt, U12(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U51(z0, z1, z2))) A__U52(tt, U12(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U52(z0, z1, z2))) A__U52(tt, U12(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(plus(z0, z1))) A__U52(tt, U12(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U12(mark(x0))), MARK(U61(z0))) A__U52(tt, U12(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U71(z0, z1, z2))) A__U52(tt, U12(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U12(mark(x0))), MARK(U72(z0, z1, z2))) A__U52(tt, U12(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U12(mark(x0))), MARK(x(z0, z1))) A__U52(tt, U12(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U12(mark(x0))), MARK(s(z0))) A__U52(tt, U12(x0), x1) -> c14(MARK(x1)) A__U52(tt, U12(x0), tt) -> c14(A__PLUS(tt, a__U12(mark(x0)))) A__U52(tt, U12(x0), 0) -> c14(A__PLUS(0, a__U12(mark(x0)))) A__U52(tt, isNat(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U11(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U52(tt, isNat(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U31(a__isNat(z0), z1)), MARK(x1)) A__U52(tt, isNat(x0), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__isNat(x0)), MARK(U11(z0, z1))) A__U52(tt, isNat(x0), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__isNat(x0)), MARK(U12(z0))) A__U52(tt, isNat(x0), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__isNat(x0)), MARK(isNat(z0))) A__U52(tt, isNat(x0), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__isNat(x0)), MARK(U21(z0))) A__U52(tt, isNat(x0), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__isNat(x0)), MARK(U31(z0, z1))) A__U52(tt, isNat(x0), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__isNat(x0)), MARK(U32(z0))) A__U52(tt, isNat(x0), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__isNat(x0)), MARK(U41(z0, z1))) A__U52(tt, isNat(x0), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__isNat(x0)), MARK(U51(z0, z1, z2))) A__U52(tt, isNat(x0), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__isNat(x0)), MARK(U52(z0, z1, z2))) A__U52(tt, isNat(x0), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__isNat(x0)), MARK(plus(z0, z1))) A__U52(tt, isNat(x0), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__isNat(x0)), MARK(U61(z0))) A__U52(tt, isNat(x0), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__isNat(x0)), MARK(U71(z0, z1, z2))) A__U52(tt, isNat(x0), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__isNat(x0)), MARK(U72(z0, z1, z2))) A__U52(tt, isNat(x0), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__isNat(x0)), MARK(x(z0, z1))) A__U52(tt, isNat(x0), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__isNat(x0)), MARK(s(z0))) A__U52(tt, isNat(0), x1) -> c14(MARK(x1)) A__U52(tt, isNat(z0), x1) -> c14(MARK(x1)) A__U52(tt, isNat(x0), tt) -> c14(A__PLUS(tt, a__isNat(x0))) A__U52(tt, isNat(x0), 0) -> c14(A__PLUS(0, a__isNat(x0))) A__U52(tt, U21(U11(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U11(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U12(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U12(mark(z0)))), MARK(x1)) A__U52(tt, U21(isNat(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__isNat(z0))), MARK(x1)) A__U52(tt, U21(U21(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U21(mark(z0)))), MARK(x1)) A__U52(tt, U21(U31(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U31(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U32(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U32(mark(z0)))), MARK(x1)) A__U52(tt, U21(U41(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U41(mark(z0), z1))), MARK(x1)) A__U52(tt, U21(U51(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U51(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(U52(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U52(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(plus(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__plus(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U21(U61(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U61(mark(z0)))), MARK(x1)) A__U52(tt, U21(U71(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U71(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(U72(z0, z1, z2)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__U72(mark(z0), z1, z2))), MARK(x1)) A__U52(tt, U21(x(z0, z1)), x1) -> c14(A__PLUS(mark(x1), a__U21(a__x(mark(z0), mark(z1)))), MARK(x1)) A__U52(tt, U21(tt), x1) -> c14(A__PLUS(mark(x1), a__U21(tt)), MARK(x1)) A__U52(tt, U21(s(z0)), x1) -> c14(A__PLUS(mark(x1), a__U21(s(mark(z0)))), MARK(x1)) A__U52(tt, U21(0), x1) -> c14(A__PLUS(mark(x1), a__U21(0)), MARK(x1)) A__U52(tt, U21(x0), U11(z0, 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U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U41(mark(x0), x1)), MARK(U31(z0, z1))) A__U52(tt, U41(x0, x1), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U41(mark(x0), x1)), MARK(U32(z0))) A__U52(tt, U41(x0, x1), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U41(mark(x0), x1)), MARK(U41(z0, z1))) A__U52(tt, U41(x0, x1), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U41(mark(x0), x1)), MARK(U51(z0, z1, z2))) A__U52(tt, U41(x0, x1), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U41(mark(x0), x1)), MARK(U52(z0, z1, z2))) A__U52(tt, U41(x0, x1), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U41(mark(x0), x1)), MARK(plus(z0, z1))) A__U52(tt, U41(x0, x1), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U41(mark(x0), x1)), MARK(U61(z0))) A__U52(tt, U41(x0, x1), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U41(mark(x0), x1)), MARK(U71(z0, z1, z2))) A__U52(tt, U41(x0, x1), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U41(mark(x0), x1)), MARK(U72(z0, z1, z2))) A__U52(tt, U41(x0, x1), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U41(mark(x0), x1)), MARK(x(z0, z1))) A__U52(tt, U41(x0, x1), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U41(mark(x0), x1)), MARK(s(z0))) A__U52(tt, U41(x0, z1), x2) -> c14(MARK(x2)) A__U52(tt, U41(x0, x1), tt) -> c14(A__PLUS(tt, a__U41(mark(x0), x1))) A__U52(tt, U41(x0, x1), 0) -> c14(A__PLUS(0, a__U41(mark(x0), x1))) A__U52(tt, U51(U11(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U52(tt, U51(U12(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U51(isNat(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__isNat(z0), x1, x2)), MARK(x3)) A__U52(tt, U51(U21(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U51(U31(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U52(tt, U51(U32(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U32(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U51(U41(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U41(mark(z0), z1), x1, x2)), MARK(x3)) A__U52(tt, U51(U51(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U51(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U51(U52(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U52(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U51(plus(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U52(tt, U51(U61(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U61(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U51(U71(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U71(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U51(U72(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__U72(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U51(x(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U52(tt, U51(tt, x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(tt, x1, x2)), MARK(x3)) A__U52(tt, U51(s(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(s(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U51(0, x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U51(0, x1, x2)), MARK(x3)) A__U52(tt, U51(x0, x1, x2), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U51(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U52(tt, U51(x0, x1, x2), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(U12(z0))) A__U52(tt, U51(x0, x1, x2), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U51(mark(x0), x1, x2)), MARK(isNat(z0))) A__U52(tt, U51(x0, x1, x2), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(U21(z0))) A__U52(tt, U51(x0, x1, x2), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U51(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U52(tt, U51(x0, x1, x2), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(U32(z0))) A__U52(tt, U51(x0, x1, x2), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U51(mark(x0), x1, x2)), MARK(U41(z0, z1))) A__U52(tt, U51(x0, x1, x2), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U51(mark(x0), x1, x2)), MARK(U51(z0, z1, z2))) A__U52(tt, U51(x0, x1, x2), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U51(mark(x0), x1, x2)), MARK(U52(z0, z1, z2))) A__U52(tt, U51(x0, x1, x2), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U51(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U52(tt, U51(x0, x1, x2), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(U61(z0))) A__U52(tt, U51(x0, x1, x2), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U51(mark(x0), x1, x2)), MARK(U71(z0, z1, z2))) A__U52(tt, U51(x0, x1, x2), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U51(mark(x0), x1, x2)), MARK(U72(z0, z1, z2))) A__U52(tt, U51(x0, x1, x2), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U51(mark(x0), x1, x2)), MARK(x(z0, z1))) A__U52(tt, U51(x0, x1, x2), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U51(mark(x0), x1, x2)), MARK(s(z0))) A__U52(tt, U51(x0, z1, z2), x3) -> c14(MARK(x3)) A__U52(tt, U51(x0, x1, x2), tt) -> c14(A__PLUS(tt, a__U51(mark(x0), x1, x2))) A__U52(tt, U51(x0, x1, x2), 0) -> c14(A__PLUS(0, a__U51(mark(x0), x1, x2))) A__U52(tt, U52(U11(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U11(mark(z0), z1), x1, x2)), MARK(x3)) A__U52(tt, U52(U12(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U12(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U52(isNat(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__isNat(z0), x1, x2)), MARK(x3)) A__U52(tt, U52(U21(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U21(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U52(U31(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U31(mark(z0), z1), x1, x2)), MARK(x3)) A__U52(tt, U52(U32(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U32(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U52(U41(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U41(mark(z0), z1), x1, x2)), MARK(x3)) A__U52(tt, U52(U51(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U51(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U52(U52(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U52(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U52(plus(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__plus(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U52(tt, U52(U61(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U61(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U52(U71(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U71(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U52(U72(z0, z1, z2), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__U72(mark(z0), z1, z2), x1, x2)), MARK(x3)) A__U52(tt, U52(x(z0, z1), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(a__x(mark(z0), mark(z1)), x1, x2)), MARK(x3)) A__U52(tt, U52(tt, x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(tt, x1, x2)), MARK(x3)) A__U52(tt, U52(s(z0), x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(s(mark(z0)), x1, x2)), MARK(x3)) A__U52(tt, U52(0, x1, x2), x3) -> c14(A__PLUS(mark(x3), a__U52(0, x1, x2)), MARK(x3)) A__U52(tt, U52(x0, x1, x2), U11(z0, z1)) -> c14(A__PLUS(a__U11(mark(z0), z1), a__U52(mark(x0), x1, x2)), MARK(U11(z0, z1))) A__U52(tt, U52(x0, x1, x2), U12(z0)) -> c14(A__PLUS(a__U12(mark(z0)), a__U52(mark(x0), x1, x2)), MARK(U12(z0))) A__U52(tt, U52(x0, x1, x2), isNat(z0)) -> c14(A__PLUS(a__isNat(z0), a__U52(mark(x0), x1, x2)), MARK(isNat(z0))) A__U52(tt, U52(x0, x1, x2), U21(z0)) -> c14(A__PLUS(a__U21(mark(z0)), a__U52(mark(x0), x1, x2)), MARK(U21(z0))) A__U52(tt, U52(x0, x1, x2), U31(z0, z1)) -> c14(A__PLUS(a__U31(mark(z0), z1), a__U52(mark(x0), x1, x2)), MARK(U31(z0, z1))) A__U52(tt, U52(x0, x1, x2), U32(z0)) -> c14(A__PLUS(a__U32(mark(z0)), a__U52(mark(x0), x1, x2)), MARK(U32(z0))) A__U52(tt, U52(x0, x1, x2), U41(z0, z1)) -> c14(A__PLUS(a__U41(mark(z0), z1), a__U52(mark(x0), x1, x2)), MARK(U41(z0, z1))) A__U52(tt, U52(x0, x1, x2), U51(z0, z1, z2)) -> c14(A__PLUS(a__U51(mark(z0), z1, z2), a__U52(mark(x0), x1, x2)), MARK(U51(z0, z1, z2))) A__U52(tt, U52(x0, x1, x2), U52(z0, z1, z2)) -> c14(A__PLUS(a__U52(mark(z0), z1, z2), a__U52(mark(x0), x1, x2)), MARK(U52(z0, z1, z2))) A__U52(tt, U52(x0, x1, x2), plus(z0, z1)) -> c14(A__PLUS(a__plus(mark(z0), mark(z1)), a__U52(mark(x0), x1, x2)), MARK(plus(z0, z1))) A__U52(tt, U52(x0, x1, x2), U61(z0)) -> c14(A__PLUS(a__U61(mark(z0)), a__U52(mark(x0), x1, x2)), MARK(U61(z0))) A__U52(tt, U52(x0, x1, x2), U71(z0, z1, z2)) -> c14(A__PLUS(a__U71(mark(z0), z1, z2), a__U52(mark(x0), x1, x2)), MARK(U71(z0, z1, z2))) A__U52(tt, U52(x0, x1, x2), U72(z0, z1, z2)) -> c14(A__PLUS(a__U72(mark(z0), z1, z2), a__U52(mark(x0), x1, x2)), MARK(U72(z0, z1, z2))) A__U52(tt, U52(x0, x1, x2), x(z0, z1)) -> c14(A__PLUS(a__x(mark(z0), mark(z1)), a__U52(mark(x0), x1, x2)), MARK(x(z0, z1))) A__U52(tt, U52(x0, x1, x2), s(z0)) -> c14(A__PLUS(s(mark(z0)), a__U52(mark(x0), x1, x2)), MARK(s(z0))) A__U52(tt, U52(x0, z1, z2), x3) -> c14(MARK(x3)) A__U52(tt, U52(x0, x1, x2), tt) -> c14(A__PLUS(tt, a__U52(mark(x0), x1, x2))) A__U52(tt, U52(x0, x1, x2), 0) -> c14(A__PLUS(0, a__U52(mark(x0), x1, x2))) K tuples:none Defined Rule Symbols: a__U11_2, a__U12_1, a__U21_1, a__U31_2, a__U32_1, a__U41_2, a__U51_3, a__U52_3, a__U61_1, a__U71_3, a__U72_3, a__isNat_1, a__plus_2, a__x_2, mark_1 Defined Pair Symbols: A__U41_2, MARK_1, A__U11_2, A__U31_2, A__ISNAT_1, A__X_2, A__U51_3, A__U52_3, A__U71_3, A__U72_3, A__PLUS_2 Compound Symbols: c10_1, c38_1, c53_1, c_1, c6_1, c27_1, c33_1, c37_1, c39_1, c41_1, c47_1, c12_1, c14_2, c14_1, c15_2, c15_1, c19_2, c19_1, c21_3, c21_1, c21_2, c22_3, c22_2, c23_2, c23_1, c26_2, c26_1, c28_2, c28_1, c30_2, c30_1, c31_2, c31_1, c34_2, c34_1, c36_2, c36_1, c1_1, c40_2, c40_1, c2_1, c42_2, c42_1, c43_2, c43_1, c44_2, c44_1, c45_2, c45_1, c46_2, c46_1, c48_2, c48_1, c49_2, c49_1, c50_2, c50_1, c51_2, c51_1, c12_2